Question

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?

Answer 1

To form a compound inequality for this problem, let's denote the price of the color printer as x.

The rebate of $35 can be seen as a reduction of the price x, so we have x - 35 as the price after the rebate.

Given that the price of the color printer ranges from $180 to $275, we can write the inequalities:

$180 ≤ x ≤ $275

To find out if Sara can stay within her budget of $150, we need to check if the price after the rebate, x - 35, is less than or equal to $150:

x - 35 ≤ $150

Now we can solve the inequality:

Adding 35 to both sides of the inequality: x ≤ $150 + 35
x ≤ $185

From the given inequalities, we know that $180 ≤ x, so it is possible that x is less than or equal to $185. Therefore, it is possible for Sara to stay within her budget of $150 for the printer, but it depends on the specific prices of the color printers she is considering.