Question

robert goes to the warehouse store to purchase items for his upcoming birthday party. when he returned from the store, he realized that some of his purchased goods were contaminated and so he would not need them. after deciding on the necessary items and returning $44 worth of goods, his total amount spent was less than $160.

part a: write an equation to determine, a, the possible amount of money originally spent at the store.

part b: determine a, the possible amount of money robert originally spent at the warehouse store.

Explanation:

Step1: Define variable and relationship

Let $a$ = original amount spent. After returning $\$44$, the remaining spent amount is $a - 44$, which is less than $\$160$.

Step2: Write the inequality

$a - 44 < 160$

Step3: Solve for $a$

Add 44 to both sides:
$a - 44 + 44 < 160 + 44$
$a < 204$
Also, since he returned $\$44$, $a$ must be greater than 44 (he couldn't return more than he spent). So $44 < a < 204$.

Answer:

Part A: $a - 44 < 160$
Part B: $44 < a < 204$ (Robert originally spent more than $\$44$ and less than $\$204$)