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Chapter 11

Algebra (And When to Use It)

Educators


Problem 1

The original selling price of an item at a store is 40 percent more than the cost of the item to the retailer, If the retailer reduces the price of the item by 15 percent of the original selling price, then the difference between the reduced price and the cost of the item to the retailer is what percent of the cost of the item to the retailer?

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Problem 2

$$x^{2}+8 x=-7$$
Quantity $\mathbf{A}$
$x$
Quantity_B
0
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 3

If $3^{3} \times 9^{12}=3^{x},$ what is the value of $x ?$

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Problem 4

If $A=2 x-(y-2 c)$ and $B=(2 x-y)-2 c,$ then $A-B=$
a. $-2 y$
b. $-4 c$
c. 0
d. $2 y$
e. $4 c$

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Problem 5

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many small cans does she purchase?
a. 35
b. 45
c. 72
d. 99
e. 208

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Problem 6

If $6 k-5 l=27$ and $3 l-2 k=-13$ and $5 k-5 l=j,$ what is the value of $j ?$

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Problem 7

If $a$ is multiplied by 3 and the result is 4 less than 6 times $b,$ what is the value of $a-2 b ?$
a. -12
b. $-\frac{4}{3}$
c. $-\frac{3}{4}$
d. $\frac{4}{3}$
e. 12

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Problem 8

Quantity $\mathbf{A}$
$$\frac{2^{-4}}{4^{-2}}$$
Quantity_B
$$\frac{\sqrt{64}}{-2^{3}}$$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 9

$$11 x+14 y=30 \text { and } 3 x+4 y=12$$
Quantity $\mathbf{A}$
$x+y$
Quantity $\mathbf{B}$
\[
(x+y)^{-2}
\]
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 10

If $x=3 a$ and $y=9 b,$ then all of the following are equal to $2(x+y)$ EXCEPT
a. $3(2 a+6 b)$
b. $6(a+3 b)$
c. $24\left(\frac{1}{4} a+\frac{3}{4} b\right)$
d. $\frac{1}{3}(18 a+54 b)$
e. $12\left(\frac{1}{2} a+\frac{3}{4} b\right)$

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