Question

Ruth wants to purchase a new video game that costs $59.00 and several bags of chips, c, that sell for $1.99 each. She can spend no more than $75.00. The inequality
1.99
c
+
59
≤
75
represents this situation.



Which of the following shows the graph of the solution set of this inequality and the best interpretation of the solution?




image.png
Ruth can buy up to 8 bags of chips.


image.png
Ruth can buy up to 8.04 bags of chips.


image.png
Ruth can buy up to 8.04 bags of chips.


image.png
Ruth can buy up to 9 bags of chips.

Answer 1

Solve 1.99c + 59 ≤ 75:
1.99c ≤ 16, so c ≤ 16/1.99 ≈ 8.0402.

The solution set is c ≤ 8.0402 (graph: closed dot at 8.0402 and shading to the left). Because c counts whole bags, she can buy at most 8 bags.

So the choice that shows c ≤ 8.04 and states “Ruth can buy up to 8 bags of chips.” is correct.