Office Max is offering a $35 mail in rebate on all color printers. Sara is looking at a few different
color printers that rang in price from $180 to $275. How much can she plan to pay after the
rebate? Form a compoun inequality to represent this problem and solve. Can she stay with in
her budget of $150 for the printer? Why or why not?
Let x be the price of the color printer.
The inequality can be formed as follows: 180 ≤ x ≤ 275.
After the rebate, Sara will pay x - 35.
To solve the inequality, subtract 35 from all parts: 180 - 35 ≤ x - 35 ≤ 275 - 35.
Simplify: 145 ≤ x - 35 ≤ 240.
Add 35 to all parts: 145 + 35 ≤ x - 35 + 35 ≤ 240 + 35.
Simplify: 180 ≤ x ≤ 275.
Therefore, Sara can stay within her budget. If her budget is $150, then x should be less than or equal to $150. However, in the given range of prices for color printers, the lowest price is $180. Therefore, Sara cannot stay within her budget of $150 for the printer.