Question

Sahib wants to spend at most $ 8.50 on school supplies. He needs to purchase a binder, which costs $ 6.89 , and wants to spend the rest on pens, which cost $ 0.59 each. Which inequality represents this situation, where x is the number of pens Sahib can buy?

Answer 1

The inequality representing the number of pens Sahib can buy with his budget is $6.89 + $0.59x ≤ $8.50. By subtracting the cost of the binder from the budget and dividing by the cost per pen, we find that Sahib can purchase at most 2 pens within his budget.

Step-by-step explanation:

The student's question is about determining the inequality that represents the budget problem faced by Sahib when buying school supplies. To set up the inequality, we need to consider the total amount Sahib is willing to spend, which is $8.50, the cost of the binder he needs to buy at $6.89, and the cost per pen, which is $0.59. The inequality that represents the situation where x is the number of pens Sahib can buy is:

$6.89 + $0.59x ≤ $8.50

To solve for x, we can rearrange the inequality to find the maximum number of pens Sahib can purchase. Here's the step-by-step explanation:

1. Subtract the cost of the binder from Sahib's total budget: $8.50 - $6.89 = $1.61.
2. Divide the remaining budget by the cost per pen: $1.61 / $0.59 ≈ 2.73.
3. Since Sahib cannot purchase a fraction of a pen, we round down to the nearest whole number, meaning Sahib can buy at most 2 pens.

The inequality shows us the relationship between the cost of pens and Sahib's spending limit. It also implies that the number of pens, x, must be an integer since you cannot buy a fraction of a pen.