Q68 - Algebra 2

Question

SCHOOL SHOPPING

For exercise 68 and 69, use the graph at the right.

Illustrate the Distributive Property by writing two expression to represent the amount that the average student spends shopping for school at specialty stores and department stores.

Step-by-Step Solution

Answer

Two expression to represent the amount that the average student spends shopping for school at specialty stores and department stores are

$A=\left(0.36\times 113\right)+\left(0.19\times 113\right)$ and $A=\left(0.36+0.19\right)\times 113$

Step 1 - Observations from image

Amount average student contributed is $\$113$

Percentage of amount spend by students for shopping at specialty stores is 36% 

Percentage of amount spend by students for shopping at department stores is 19%

Step 2 - Write first expression

Since, average student spends 36% of $\$113$ at specialty store and 19% of $\$113$ at departmental stores.

To get amount (A) add the terms

$\begin{array}{c}A=\left(36\%\times 113\right)+\left(19\%\times 113\right)\\ A=\left(0.36\times 113\right)+\left(0.19\times 113\right)\end{array}$

Step 3 - Write second expression

For any real numbers a, b, and c distributive property is 

$a\left(b+c\right)=ab+ac\text{ and }\left(b+c\right)a=ba+ca$

For second expression, use distributive property in first expression

$A=\left(0.36+0.19\right)\times 113$