College Algebra

Michael Sullivan

Chapter 8 Systems of Equations and Inequalities - all with Video Answers

Educators

Section 1

Systems of Linear Equations: Substitution and Elimination

00:59

Problem 1

Solve the equation: $3 x+4=8-x$

Brandon Fox

Numerade Educator

02:05

Problem 2

(a) Graph the line: $3 x+4 y=12$
(b) What is the slope of a line parallel to this line?

Brandon Fox

Numerade Educator

00:17

Problem 3

If a system of equations has no solution, it is said to be _________.

Brandon Fox

Numerade Educator

00:32

Problem 4

If a system of equations has one solution, the system is ________ and the equations are _______.

Brandon Fox

Numerade Educator

00:10

Problem 5

If the solution to a system of two linear equations containing two unknowns is $x=3, y=-2,$ then the lines intersect at the point ________.

Brandon Fox

Numerade Educator

00:32

Problem 6

If the lines that make up a system of two linear equations are coincident, then the system is ________ and the equations are __________.

Brandon Fox

Numerade Educator

01:06

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{l} 2 x-y=5 \\ 5 x+2 y=8 \end{array}\right.\\ &x=2, y=-1 ;(2,-1) \end{aligned}$$

Kelly Hughes

Numerade Educator

00:49

Problem 8

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{rr} 3 x+2 y= & 2 \\ x-7 y= & -30 \end{array}\right.\\ &x=-2, y=4 ;(-2,4) \end{aligned}$$

Brandon Fox

Numerade Educator

00:57

Problem 9

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{l} 3 x-4 y=4 \\ \frac{1}{2} x-3 y=-\frac{1}{2} \end{array}\right.\\ &x=2, y=\frac{1}{2} ;\left(2, \frac{1}{2}\right) \end{aligned}$$

Brandon Fox

Numerade Educator

01:20

Problem 10

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{lr} 2 x+\frac{1}{2} y & =0 \\ 3 x-4 y & =-\frac{19}{2} \end{array}\right.\\ &x=-\frac{1}{2}, y=2 ;\left(-\frac{1}{2}, 2\right) \end{aligned}$$

Kelly Hughes

Numerade Educator

00:30

Problem 11

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{l} x-y=3 \\ \frac{1}{2} x+y=3 \end{array}\right.\\ &x=4, y=1 ;(4,1) \end{aligned}$$

Brandon Fox

Numerade Educator

00:41

Problem 12

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{r} x-y=3 \\ -3 x+y=1 \end{array}\right.\\ &x=-2, y=-5 ;(-2,-5) \end{aligned}$$

Brandon Fox

Numerade Educator

01:23

Problem 13

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{rr} 3 x+3 y+2 z= & 4 \\ x-y-z= & 0 \\ 2 y-3 z= & -8 \end{array}\right.\\ &x=1, y=-1, z=2\\ &(1,-1,2) \end{aligned}$$

Kelly Hughes

Numerade Educator

01:10

Problem 14

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{r} 4 x \quad-\quad z=7 \\ 8 x+5 y-z=0 \\ -x-y+5 z=6 \end{array}\right.\\ &x=2, y=-3, z=1\\ &(2,-3,1) \end{aligned}$$

Brandon Fox

Numerade Educator

01:32

Problem 15

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{l} 3 x+3 y+2 z=4 \\ x-3 y+z=10 \\ 5 x-2 y-3 z=8 \end{array}\right.\\ &x=2, y=-2, z=2 ;(2,-2,2) \end{aligned}$$

Brandon Fox

Numerade Educator

01:15

Problem 16

verify that the values of the variables listed are solutions of the system of equations.
$$\begin{aligned} &\left\{\begin{array}{rr} 4 x-5 z= & 6 \\ 5 y-z= & -17 \\ -x-6 y+5 z= & 24 \end{array}\right.\\ &x=4, y=-3, z=2 ;(4,-3,2) \end{aligned}$$

Brandon Fox

Numerade Educator

01:13

Problem 17

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
x+y=8 \\
x-y=4
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:42

Problem 18

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
x+2 y=-7 \\
x+y=-3
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:55

Problem 19

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
5 x-y=21 \\
2 x+3 y=-12
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:15

Problem 20

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x+3 y= & 5 \\
2 x-3 y= & -8
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:00

Problem 21

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
3 x &=24 \\
x+2 y &=0
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

01:21

Problem 22

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
4 x+5 y &=-3 \\
-2 y &=-8
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:28

Problem 23

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x-6 y=2 \\
5 x+4 y=1
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:48

Problem 24

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
2 x+4 y=\frac{2}{3} \\
3 x-5 y=-10
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:45

Problem 25

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
2 x+y=1 \\
4 x+2 y=3
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:35

Problem 26

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{r}
x-y=5 \\
-3 x+3 y=2
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:04

Problem 27

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{c}
2 x-y=0 \\
4 x+2 y=12
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:37

Problem 28

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x+3 y=-1 \\
4 x+y=\frac{8}{3}
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:20

Problem 29

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{r}
x+2 y=4 \\
2 x+4 y=8
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:15

Problem 30

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x-y=7 \\
9 x-3 y=21
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:55

Problem 31

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-3 y &=-1 \\
10 x+y &=11
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:08

Problem 32

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
3 x-2 y=0 \\
5 x+10 y=4
\end{array}\right.$$

Kelly Hughes

Numerade Educator

02:10

Problem 33

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{r}
2 x+3 y=6 \\
x-y=\frac{1}{2}
\end{array}\right.$$

Andrija Isakov

Numerade Educator

02:04

Problem 34

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{2} x+y=-2 \\
x-2 y=8
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:38

Problem 35

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{2} x+\frac{1}{3} y=3 \\
\frac{1}{4} x-\frac{2}{3} y=-1
\end{array}\right.$$

Kelly Hughes

Numerade Educator

04:19

Problem 36

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{3} x-\frac{3}{2} y=-5 \\
\frac{3}{4} x+\frac{1}{3} y=11
\end{array}\right.$$

Kelly Hughes

Numerade Educator

01:55

Problem 37

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
3 x-5 y &=3 \\
15 x+5 y &=21
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:10

Problem 38

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-y &=-1 \\
x+\frac{1}{2} y &=\frac{3}{2}
\end{aligned}\right.$$

Andrija Isakov

Numerade Educator

05:32

Problem 39

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{1}{x}+\frac{1}{y}=8 \\
\frac{3}{x}-\frac{5}{y}=0
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:24

Problem 40

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
\frac{4}{x}-\frac{3}{y}=0 \\
\frac{6}{x}+\frac{3}{2 y}=2
\end{array}\right.$$

Andrija Isakov

Numerade Educator

04:09

Problem 41

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x-y &=6 \\
2 x &-3 z=16 \\
2 y+z &=4
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

04:27

Problem 42

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
2 x+y & =-4 \\
-2 y+4 z & =0 \\
3 x & -2 z=-11
\end{array}\right.$$

Kelly Hughes

Numerade Educator

09:25

Problem 43

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x-2 y+3 z= & 7 \\
2 x+y+z= & 4 \\
-3 x+2 y-2 z= & -10
\end{array}\right.$$

Kelly Hughes

Numerade Educator

04:56

Problem 44

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
2 x+y-3 z= & 0 \\
-2 x+2 y+z= & -7 \\
3 x-4 y-3 z= & 7
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:43

Problem 45

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x-y-z &=1 \\
2 x+3 y+z &=2 \\
3 x+2 y &=0
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

03:30

Problem 46

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{l}
2 x-3 y-z=0 \\
-x+2 y+z=5 \\
3 x-4 y-z=1
\end{array}\right.$$

Kelly Hughes

Numerade Educator

03:38

Problem 47

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x-y-z= & 1 \\
-x+2 y-3 z= & -4 \\
3 x-2 y-7 z= & 0
\end{array}\right.$$

Andrija Isakov

Numerade Educator

03:04

Problem 48

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-3 y-z &=0 \\
3 x+2 y+2 z &=2 \\
x+5 y+3 z &=2
\end{aligned}\right.$$

Kelly Hughes

Numerade Educator

02:40

Problem 49

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
2 x-2 y+3 z &=6 \\
4 x-3 y+2 z &=0 \\
-2 x+3 y-7 z &=1
\end{aligned}\right.$$

Andrija Isakov

Numerade Educator

04:28

Problem 50

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
3 x-2 y+2 z= & 6 \\
7 x-3 y+2 z= & -1 \\
2 x-3 y+4 z= & 0
\end{array}\right.$$

Kelly Hughes

Numerade Educator

04:48

Problem 51

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x+y-z= & 6 \\
3 x-2 y+z= & -5 \\
x+3 y-2 z= & 14
\end{array}\right.$$

Kelly Hughes

Numerade Educator

03:14

Problem 52

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{array}{rr}
x-y+z= & -4 \\
2 x-3 y+4 z= & -15 \\
5 x+y-2 z= & 12
\end{array}\right.$$

Andrija Isakov

Numerade Educator

04:22

Problem 53

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x+2 y-z &=-3 \\
2 x-4 y+z &=-7 \\
-2 x+2 y-3 z &=4
\end{aligned}\right.$$

Andrija Isakov

Numerade Educator

05:26

Problem 54

solve each system of equations. If the system has no solution, say that it is inconsistent.
$$\left\{\begin{aligned}
x+4 y-3 z &=-8 \\
3 x-y+3 z &=12 \\
x+y+6 z &=1
\end{aligned}\right.$$

Andrija Isakov

Numerade Educator

01:13

Problem 55

The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.

Brandon Fox

Numerade Educator

02:14

Problem 56

The length of fence required to enclose a rectangular field is 3000 meters What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Brandon Fox

Numerade Educator

02:38

Problem 57

Orbital Launches In 2005 there was a total of 55 commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was one more than twice the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches in 2005 .

Kelly Hughes

Numerade Educator

06:19

Problem 58

Movie Theater Tickets $A$ movie theater charges $\$ 9.00$ for adults and $\$ 7.00$ for senior citizens. On a day when 325 people paid an admission, the total receipts were $\$ 2495 .$ How many who paid were adults? How many were seniors?

Andrija Isakov

Numerade Educator

03:42

Problem 59

Mixing Nuts $\quad$ A store sells cashews for $\$ 5.00$ per pound and peanuts for $\$ 1.50$ per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $\$ 3.00$ per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Andrija Isakov

Numerade Educator

02:15

Problem 60

Financial Planning A recently retired couple needs $\$ 12,000$ per year to supplement their Social Security. They have $\$ 150,000$ to invest to obtain this income. They have decided on two investment options: AA bonds yielding $10 \%$ per annum and a Bank Certificate yielding $5 \%$.
(a) How much should be invested in each to realize exactly $\$ 12,000 ?$
(b) If, after 2 years, the couple requires $\$ 14,000$ per year in income, how should they reallocate their investment to achieve the new amount?

Brandon Fox

Numerade Educator

03:50

Problem 61

Computing Wind Speed With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.

Laneshia Lamb

Numerade Educator

07:07

Problem 62

Computing Wind Speed The average airspeed of a singleengine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?

Stephanie Carter

Numerade Educator

05:28

Problem 63

Restaurant Management $A$ restaurant manager wants to purchase 200 sets of dishes. One design costs $\$ 25$ per set, while another costs $\$ 45$ per set. If she only has $\$ 7400$ to spend, how many of each design should be ordered?

Andrija Isakov

Numerade Educator

05:30

Problem 64

cost of Fast Food One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $\$ 35.00 .$ A second bought 7 hot dogs and 4 soft drinks at a cost of $\$ 25.25 .$ What is the cost of a single hot dog? A single soft drink?

Andrija Isakov

Numerade Educator

09:29

Problem 65

Computing a Refund The grocery store we use does not mark prices on its goods. My wife went to this store, bought three 1-pound packages of bacon and two cartons of eggs, and paid a total of $\$ 13.45 .$ Not knowing that she went to the store, I also went to the same store, purchased two 1 -pound packages of bacon and three cartons of eggs, and paid a total of $\$ 11.45 .$ Now we want to return two 1 -pound pack. ages of bacon and two cartons of eggs. How much will be refunded?

Stephanie Carter

Numerade Educator

08:53

Problem 66

Finding the Current of a Stream Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours. Find Pamela's average speed in still water. How fast is the current? (Assume that Pamela's speed is the same in each direction.)

Stephanie Carter

Numerade Educator

02:32

Problem 67

Pharmacy A doctor's prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: one contains $20 \%$ vitamin $\mathrm{C}$ and $30 \%$ vitamin $\mathrm{D}$, the other $40 \%$ vitamin $\mathrm{C}$ and $20 \%$ vitamin D. How many milligrams of each compound should be mixed to fill the prescription?

Dharmendra Jain

Numerade Educator

01:49

Problem 68

Pharmacy A doctor's prescription calls for the creation of pills that contain 12 units of vitamin $B_{12}$ and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills: one contains $20 \%$ vitamin $\mathrm{B}_{12}$ and $30 \%$ vitamin $\mathrm{E}$, the other $40 \%$ vitamin $\mathrm{B}_{12}$ and $20 \%$ vitamin E. How many units of each powder should be mixed in each pill?

Dharmendra Jain

Numerade Educator

03:49

Problem 69

Curve Fitting Find real numbers $a, b,$ and $c$ so that the graph of the function $y=a x^{2}+b x+c$ contains the points $(-1,4),(2,3),$ and $(0,1)$

Andrija Isakov

Numerade Educator

04:48

Problem 70

Curve Fitting Find real numbers $a, b,$ and $c$ so that the graph of the function $y=a x^{2}+b x+c$ contains the points $(-1,-2),(1,-4),$ and $(2,4)$

Andrija Isakov

Numerade Educator

02:51

Problem 71

IS-LM Model in Economics In economics, the IS curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for goods in the economy. The LM curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for money in the economy. In an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations
$$ \left\{\begin{array}{l} 0.06 Y-5000 r=240 \\ 0.06 Y+6000 r=900 \end{array}\right. $$
Find the equilibrium level of income and interest rates.

Melissa Barry

Numerade Educator

02:57

Problem 72

IS-LM Model in Economics In economics, the IS curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for goods in the cconomy. The LM curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for money in the economy. In an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations
$$ \left\{\begin{array}{l} 0.05 Y-1000 r=10 \\ 0.05 Y+800 r=100 \end{array}\right. $$
Find the equilibrium level of income and interest rates.

Melissa Barry

Numerade Educator

04:01

Problem 73

Electricity: Kirchhoff's Rules An application of Kirchhoffs Rules to the circuit shown on page 555 results in the following system of equations:
$$ \left\{\begin{aligned} I_{2} &=I_{1}+I_{3} \\ 5-3 I_{1}-5 I_{2} &=0 \\ 10-5 I_{2}-7 I_{3} &=0 \end{aligned}\right. $$
Find the currents $I_{1}, I_{2},$ and $I_{3}$

Andrija Isakov

Numerade Educator

10:53

Problem 74

Electricity: Kirchhoffs Rules An application of Kirchhoffs Rules to the circuit shown results in the following system of equations:
$$ \left\{\begin{aligned} I_{3} &=I_{1}+I_{2} \\ 8 &=4 I_{3}+6 I_{2} \\ 8 I_{1} &=4+6 I_{2} \end{aligned}\right. $$
Find the currents $I_{1}, I_{2},$ and $I_{3}$

Stephanie Carter

Numerade Educator

13:32

Problem 75

Theater Revenues A Broadway theater has 500 seats. divided into orchestra, main, and balcony seating. Orchestra seats sell for $\$ 50,$ main seats for $\$ 35,$ and balcony seats for S25. If all the seats are sold, the gross revenue to the theater is $\$ 17,100 .$ If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $\$ 14,600 .$ How many are there of each kind of seat?

Stephanie Carter

Numerade Educator

13:01

Problem 76

Theater Revenues A movie theater charges $\$ 8.00$ for adults, $\$ 4.50$ for children, and $\$ 6.00$ for senior citizens. One day the theater sold 405 tickets and collected $\$ 2320$ in receipts. Twice as many children's tickets were sold as adult tickets. How many adults, children, and senior citizens went to the theater that day?

Stephanie Carter

Numerade Educator

18:13

Problem 77

Nutrition A dietitian wishes a patient to have a meal that has 66 grams (g) of protein, $94.5 \mathrm{g}$ of carbohydrates, and 910 milligrams (mg) of calcium. The hospital food service tells the dietitian that the dinner for today is chicken, corn, and $2 \%$ milk. Each serving of chicken has $30 \mathrm{g}$ of protein, 35 g of carbohydrates, and 200 mg of calcium. Each serving of corn has $3 \mathrm{g}$ of protein, $16 \mathrm{g}$ of carbohydrates, and $10 \mathrm{mg}$ of calcium. Each glass of $2 \%$ milk has 9 g of protein, 13 g of carbohydrates, and $300 \mathrm{mg}$ of calcium. How many servings of each food should the dietitian provide for the patient?

Stephanie Carter

Numerade Educator

13:18

Problem 78

Investments Kelly has $\$ 20,000$ to invest. As her financial planner, you recommend that she diversify into three investments: Treasury bills that yield $5 \%$ simple interest, Treasury bonds that yicld $7 \%$ simple interest, and corporate bonds that yield $10 \%$ simple interest. Kelly wishes to earn $\$ 1390$ per year in income. Also, Kelly wants her investment in Treasury bills to be $\$ 3000$ more than her investment in corporate bonds. How much money should Kelly place in each investment?

Stephanie Carter

Numerade Educator

03:27

Problem 79

Prices of Fast Food One group of customers bought 8 deluxe hamburgers, 6 orders of large fries, and 6 large colas for $\$ 26.10 .$ A second group ordered 10 deluxe hamburgers, 6 large fries, and 8 large colas and paid $\$ 31.60 .$ Is there sufficient information to determine the price of cach food item? If not, construct a table showing the various possibilities. Assume that the hamburgers cost between $\$ 1.75$ and $\$ 2.25,$ the fries between $\$ 0.75$ and $\$ 1.00,$ and the colas between $\$ 0.60$ and $\$ 0.90$

Maria Santiago

Numerade Educator

13:04

Problem 80

Prices of Fast Food Use the information given in Problem $79 .$ Suppose that a third group purchased 3 deluxe hamburgers, 2 large fries, and 4 large colas for $\$ 10.95 .$ Now is there sufficient information to determine the price of each food item? If so, determine each price.

Stephanie Carter

Numerade Educator

14:45

Problem 81

Painting a House Three painters, Beth, Bill, and Edie, working together, can paint the exterior of a home in 10 hours (hr). Bill and Edie together have painted a similar house in 15 hr. One day, all three worked on this same kind of house for 4 hr, after which Edie left. Beth and Bill required 8 more hr to finish. Assuming no gain or loss in efficiency, how long should it take each person to complete such a job alone?

Stephanie Carter

Numerade Educator

02:27

Problem 82

Make up a system of three linear equations containing three variables that has:
(a) No solution
(b) Exactly one solution
(c) Infinitely many solutions Give the three systems to a friend to solve and critique.

Dharmendra Jain

Numerade Educator

02:15

Problem 83

Write a brief paragraph outlining your strategy for solving a system of two linear equations containing two variables.

Dharmendra Jain

Numerade Educator

02:09

Problem 84

Do you prefer the method of substitution or the method of elimination for solving a system of two linear equations containing two variables? Give reasons.

Brandon Fox

Numerade Educator