Office Max is offering a $35 rebate on all color printers. Sara is looking at a few different color printers that range in price from $170 to $300. How 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 $125 for the printer? Why or Why not?

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Answer 1

Part A:

Let's assume the price of the color printer is represented by the variable x.

The given information states that Office Max is offering a $35 rebate on all color printers. This means, after the rebate, Sara will have to pay the remaining cost of the printer.

To calculate the remaining cost, we subtract the rebate from the price of the printer:

Remaining cost = Price of the printer - Rebate = x - $35

The problem states that the price of the color printers range from $170 to $300. So we can write the following inequality:

$170 ≤ x ≤ $300

Now we can substitute the value of x in the inequality above with the remaining cost:

$170 ≤ x ≤ $300
$170 ≤ (x - $35) ≤ $300

Simplifying the inequality:

$170 + $35 ≤ x ≤ $300 + $35
$205 ≤ x ≤ $335

Therefore, the compound inequality to represent the problem is:

$205 ≤ x ≤ $335

Part B:

Sara's budget for the printer is $125. We need to determine if any of the prices within the range $205 to $335 fall within her budget.

If x represents the price of the printer, and the remaining cost after the rebate is x - $35, then we can set up the inequality:

x - $35 ≤ $125

Simplifying the inequality:

x ≤ $125 + $35
x ≤ $160

Therefore, all color printers within the price range of $205 to $335 are more expensive than Sara's budget of $125. Therefore, she cannot stay within her budget.