Algebra 1

Ron Larson, Laurie Boswell, Timothy D. Kanold

Chapter 11 Rational Equations and Functions - all with Video Answers

Educators

Section 1

Ratio and Proportion

00:53

Problem 1

Write the extremes and the means of the proportion $\frac{3}{4}=\frac{9}{12}$.

Amy Jiang

Numerade Educator

00:32

Problem 2

Write yes or no to tell whether the equation is a consequence of $\frac{a}{b}=\frac{c}{d}$.
$$
a c=b d
$$

Amy Jiang

Numerade Educator

00:28

Problem 3

Write yes or no to tell whether the equation is a consequence of $\frac{a}{b}=\frac{c}{d}$.
$$b a=d c$$

Amy Jiang

Numerade Educator

00:22

Problem 4

Write yes or no to tell whether the equation is a consequence of $\frac{a}{b}=\frac{c}{d}$.
$$a d=b c$$

Amy Jiang

Numerade Educator

00:22

Problem 5

Write yes or no to tell whether the equation is a consequence of $\frac{a}{b}=\frac{c}{d}$.
$$\frac{a}{b}=\frac{d}{c}$$

Amy Jiang

Numerade Educator

00:22

Problem 6

Write yes or no to tell whether the equation is a consequence of $\frac{a}{b}=\frac{c}{d}$.
$$\frac{b}{a}=\frac{d}{c}$$

Amy Jiang

Numerade Educator

00:47

Problem 7

Write yes or no to tell whether the equation is a consequence of $\frac{a}{b}=\frac{c}{d}$.
$$\frac{a}{d}=\frac{b}{c}$$

Amy Jiang

Numerade Educator

02:47

Problem 8

Solve the proportion $\frac{4}{x+1}=\frac{7}{2}$ two ways- using the reciprocal property and using the cross product method. Which method do you prefer? Why?

Amy Jiang

Numerade Educator

00:16

Problem 9

Solve the proportion. Check for extraneous solutions.
$$\frac{x}{3}=\frac{2}{7}$$

Amy Jiang

Numerade Educator

00:21

Problem 10

Solve the proportion. Check for extraneous solutions.
$$\frac{6}{x}=\frac{5}{3}$$

Amy Jiang

Numerade Educator

00:34

Problem 11

Solve the proportion. Check for extraneous solutions.
$$\frac{2}{2 x+1}=\frac{1}{5}$$

Amy Jiang

Numerade Educator

01:26

Problem 12

Solve the proportion. Check for extraneous solutions.
$$\frac{3}{x}=\frac{x+1}{4}$$

Amy Jiang

Numerade Educator

00:54

Problem 13

Solve the proportion. Check for extraneous solutions.
$$\frac{t-2}{t}=\frac{2}{t+3}$$

Amy Jiang

Numerade Educator

00:58

Problem 14

Solve the proportion. Check for extraneous solutions.
$$\frac{2 u-3}{4 u}=\frac{u-1}{u}$$

Amy Jiang

Numerade Educator

01:13

Use Example $5 .$ The proportion used in Example 5 compares height to length, but the situation could be described using other comparisons instead.
Set up a different proportion to represent the situation in Example 5 .

Amy Jiang

Numerade Educator

00:45

Problem 16

Use Example $5 .$ The proportion used in Example 5 compares height to length, but the situation could be described using other comparisons instead.
Solve the proportion you wrote in Exercise $15 .$ Do you get the same solution as in Example $5 ?$

Amy Jiang

Numerade Educator

00:32

Problem 17

Solve the proportion. Check for extraneous solutions.
$$\frac{16}{4}=\frac{12}{x}$$

Amy Jiang

Numerade Educator

00:38

Problem 18

Solve the proportion. Check for extraneous solutions.
$$\frac{4}{2 x}=\frac{7}{3}$$

Amy Jiang

Numerade Educator

00:22

Problem 19

Solve the proportion. Check for extraneous solutions.
$$\frac{5}{8}=\frac{c}{9}$$

Amy Jiang

Numerade Educator

00:21

Problem 20

Solve the proportion. Check for extraneous solutions.
$$\frac{x}{3}=\frac{2}{5}$$

Amy Jiang

Numerade Educator

00:33

Problem 21

Solve the proportion. Check for extraneous solutions.
$$\frac{5}{3 c}=\frac{2}{3}$$

Amy Jiang

Numerade Educator

01:02

Problem 22

Solve the proportion. Check for extraneous solutions.
$$\frac{24}{5}=\frac{9}{y+2}$$

Amy Jiang

Numerade Educator

00:37

Problem 23

Solve the proportion. Check for extraneous solutions.
$$\frac{6}{3}=\frac{x+8}{-1}$$

Amy Jiang

Numerade Educator

00:28

Problem 24

Solve the proportion. Check for extraneous solutions.
$$\frac{r+4}{3}=\frac{r}{5}$$

Amy Jiang

Numerade Educator

00:49

Problem 25

Solve the proportion. Check for extraneous solutions.
$$\frac{w+4}{2 w}=\frac{-5}{6}$$

Amy Jiang

Numerade Educator

00:57

Problem 26

Solve the proportion. Check for extraneous solutions.
$$\frac{5}{2 y}=\frac{7}{y-3}$$

Amy Jiang

Numerade Educator

00:32

Problem 27

Solve the proportion. Check for extraneous solutions.
$$\frac{x+6}{3}=\frac{x-5}{2}$$

Amy Jiang

Numerade Educator

00:31

Problem 28

Solve the proportion. Check for extraneous solutions.
$$\frac{x-2}{4}=\frac{x+10}{10}$$

Amy Jiang

Numerade Educator

00:48

Problem 29

Solve the proportion. Check for extraneous solutions.
$$\frac{8}{x+2}=\frac{3}{x-1}$$

Amy Jiang

Numerade Educator

00:39

Problem 30

Solve the proportion. Check for extraneous solutions.
$$\frac{x-3}{18}=\frac{3}{x}$$

Amy Jiang

Numerade Educator

00:37

Problem 31

Solve the proportion. Check for extraneous solutions.
$$\frac{-2}{a-7}=\frac{a}{5}$$

Amy Jiang

Numerade Educator

00:51

Problem 32

Solve the proportion. Check for extraneous solutions.
$$\frac{u}{3}=\frac{1}{2 u-1}$$

Amy Jiang

Numerade Educator

00:53

Problem 33

Solve the proportion. Check for extraneous solutions.
$$\frac{d}{d+4}=\frac{d-2}{d}$$

Amy Jiang

Numerade Educator

00:45

Problem 34

Solve the proportion. Check for extraneous solutions.
$$\frac{3 x}{4 x-1}=\frac{1}{x}$$

Amy Jiang

Numerade Educator

00:51

Problem 35

Solve the proportion. Check for extraneous solutions.
$$\frac{x-3}{x}=\frac{x}{x+6}$$

Amy Jiang

Numerade Educator

00:52

Problem 36

Solve the proportion. Check for extraneous solutions.
$$\frac{5}{m+1}=\frac{4 m}{m}$$

Amy Jiang

Numerade Educator

00:49

Problem 37

Solve the proportion. Check for extraneous solutions.
$$\frac{2}{3 t}=\frac{t-1}{t}$$

Amy Jiang

Numerade Educator

00:54

Problem 38

Solve the proportion. Check for extraneous solutions.
$$\frac{2}{6 x+1}=\frac{2 x}{1}$$

Amy Jiang

Numerade Educator

00:47

Problem 39

Solve the proportion. Check for extraneous solutions.
$$\frac{-2}{q}=\frac{q+1}{q^{2}}$$

Amy Jiang

Numerade Educator

01:40

Problem 40

Solve the proportion. Check for extraneous solutions.
$$\frac{6}{19 n}=\frac{-2}{n^{2}+2}$$

Amy Jiang

Numerade Educator

00:49

Problem 41

Use the following information. The $A r t$ is the Heart of the City fence mural project in Charlotte, North Carolina, involved artists Cordelia Williams and Paul Rousso along with 22 students in grades 11 and 12 Students created drawings on paper. Slides of the drawings were made and projected to fit onto 4 -foot-wide by 8 -foot-long sheets of plywood used for the fence panels. Students traced and later painted the enlarged images.
If the paper used for the original drawings was 11 inches wide, how long did it need to be?

Amy Jiang

Numerade Educator

01:06

Problem 42

Use the following information. The $A r t$ is the Heart of the City fence mural project in Charlotte, North Carolina, involved artists Cordelia Williams and Paul Rousso along with 22 students in grades 11 and 12 Students created drawings on paper. Slides of the drawings were made and projected to fit onto 4 -foot-wide by 8 -foot-long sheets of plywood used for the fence panels. Students traced and later painted the enlarged images.
Suppose the length of the paintbrush on the panel shown is $2 \frac{1}{2}$ feet. Use Exercise 41 to find the length of the paintbrush in the student's drawing.

Amy Jiang

Numerade Educator

01:00

Problem 43

A scale model uses a scale of $\frac{1}{16}$ inch to represent 1 foot. Explain how you can use a proportion and cross products to show that a scale of $\frac{1}{16}$ in. to 1 ft is the same as a scale of 1 in. to 192 in.

Amy Jiang

Numerade Educator

01:40

Problem 44

Use the table. It shows the results of a survey in which 100 students were asked how they spent money last week.
$$\begin{array}{|l|c|}\hline \quad \quad\quad\quad \text { Item } & \begin{array}{c}\text { Number } \\\text { of students }\end{array} \\\hline \text { Food } & 78 \\\hline \text { Clothes, accessories } & 20 \\\hline \text { Books, magazines, comics } & 15 \\\hline \text { Toys, stickers, games } & 14 \\
\hline \text { Movie tickets } & 14 \\\hline \text { Arcade games } & 14 \\\hline \text { Gifts } & 13 \\\hline \text { Movie rentals } & 13 \\\hline \text { Music } & 12 \\\hline \text { Footwear } & 11 \\\hline \text { Grooming products } & 11 \\\hline\end{array}$$
Estimate the number of students out of 500 that bought clothes or accessories in the last week.

Amy Jiang

Numerade Educator

02:17

Problem 45

Use the table. It shows the results of a survey in which 100 students were asked how they spent money last week.
$$\begin{array}{|l|c|}\hline \quad \quad\quad\quad \text { Item } & \begin{array}{c}\text { Number } \\\text { of students }\end{array} \\\hline \text { Food } & 78 \\\hline \text { Clothes, accessories } & 20 \\\hline \text { Books, magazines, comics } & 15 \\\hline \text { Toys, stickers, games } & 14 \\
\hline \text { Movie tickets } & 14 \\\hline \text { Arcade games } & 14 \\\hline \text { Gifts } & 13 \\\hline \text { Movie rentals } & 13 \\\hline \text { Music } & 12 \\\hline \text { Footwear } & 11 \\\hline \text { Grooming products } & 11 \\\hline\end{array}$$
Choose 3 items that were bought by different numbers of students. Based on the survey, how many students out of 20 would you predict to have bought each item?

Amy Jiang

Numerade Educator

00:19

Problem 46

Use the table. It shows the results of a survey in which 100 students were asked how they spent money last week.
$$\begin{array}{|l|c|}\hline \quad \quad\quad\quad \text { Item } & \begin{array}{c}\text { Number } \\\text { of students }\end{array} \\\hline \text { Food } & 78 \\\hline \text { Clothes, accessories } & 20 \\\hline \text { Books, magazines, comics } & 15 \\\hline \text { Toys, stickers, games } & 14 \\
\hline \text { Movie tickets } & 14 \\\hline \text { Arcade games } & 14 \\\hline \text { Gifts } & 13 \\\hline \text { Movie rentals } & 13 \\\hline \text { Music } & 12 \\\hline \text { Footwear } & 11 \\\hline \text { Grooming products } & 11 \\\hline\end{array}$$
Choose one item from Exercise $45 .$ Ask 20 students whether they bought that item. Compare the results with your prediction. Are the results what you expected? Explain.

Amy Jiang

Numerade Educator

01:21

Problem 47

Researchers studying fish populations at Dryden Lake in New York caught, marked, and then released 232 Chain pickerel. Later a sample of 329 Chain pickerel were caught and examined. Of these, 16 were found to be marked. Use the proportion below to estimate the total Chain pickerel population in the lake. $\frac{\text { Marked pickerel in sample }}{\text { Total pickerel in sample }}=\frac{\text { Marked pickerel in lake }}{\text { Total pickerel in lake }}$

Amy Jiang

Numerade Educator

07:14

Problem 48

Base your answers on the 1997 population data shown in the table for people 25 years and older in the United States. (TABLE CANNOT COPY).
a. Out of 200 people aged 25 years or older, about how many would you expect to have just a high school education? to have at least 4 years of college?
b. Write and solve a proportion to estimate the number of people in the United States aged 25 years or older with at least 4 years of college.
c. Suppose a town has $20,000$ residents aged 25 years or older. Write and solve a proportion to estimate the number of town residents 25 years or older who have completed at least 4 years of college.
d. Suppose another town has $15,860$ people aged 25 years or older and that 7581 of these people have completed at least 4 years of college. Explain how you can find out whether the number of college graduates in that town is typical for a town of that size.

Sonam Khatri

Numerade Educator

00:32

Problem 49

One way to prove that two proportions are equivalent is to apply the properties of equality to transform one of the proportions into the other proportion. Give a sequence of steps that transforms the proportion $\frac{a}{b}=\frac{c}{d}$ into $\frac{a}{c}=\frac{b}{d}$.

Amy Jiang

Numerade Educator

01:11

Problem 50

Copy and complete the table. If necessary, round to the nearest tenth of a percent.
$$\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline \text { Decimal } & ? & 0.2 & ? & 0.073 & 0.666 \ldots & ? & ? & 2 \\\hline \text { Percent } & 78 \% & ? & 3 \% & ? & ? & 176 \% & 110 \% & ? \\\hline\end{array}$$

Amy Jiang

Numerade Educator

00:13