Office Max is offering a $40 rebate on all color printers. Sara is looking at a few different color printers that range in price from $165 to $295. How much can she plan to pay after the rebate?

Question

Part A: Form a compound inequality to represent this problem and solve.
Part B: Can she stay within her budget of $123 for the printer? Why or why not?

Answer 1

Part A:
Let x be the price of the color printer.
The compound inequality is:
165 ≤ x ≤ 295.
After the rebate of $40, the price she would have to pay will be:
x - $40.
So, the compound inequality after the rebate is:
165 - $40 ≤ x - $40 ≤ 295 - $40.

Simplifying the compound inequality:
125 ≤ x - $40 ≤ 255.

Part B:
If Sara has a budget of $123 for the printer, then we can represent this as an inequality:
x ≤ $123.

Comparing the inequality x ≤ $123 with the compound inequality 125 ≤ x - $40 ≤ 255, we can see that x ≤ $123 satisfies the compound inequality.

Therefore, Sara can stay within her budget of $123 for the printer.