Office Max is offering a 35$ rebate on all color printers. Sarah is looking for a few different color printers that range in price 170$ to 300$. How much can she plan to pay after the rebate?

Question

Office Max is offering a 35$ rebate on all color printers. Sarah is looking for a few different color printers that range in price 170$ to 300$. How much can she plan to pay after the rebate?

Part A: Form a compound inequality to represent this problem and solve.
Part B: Can she stay within her budget of $125 for her printer? why or why not

Answer 1

Part A:

Let x be the price of the color printers.
The compound inequality to represent the problem is:
170 ≤ x ≤ 300

To calculate the price after the rebate, subtract $35 from each side of the inequality:
170 - $35 ≤ x - $35 ≤ 300 - $35
135 ≤ x - $35 ≤ 265

So, Sarah can expect to pay between $135 and $265 after the rebate.

Part B:
Since Sarah's budget is $125, she cannot stay within her budget for the printers because the minimum price after the rebate is $135, which is higher than her budget.

Answer 2

Part A:

Let "x" represent the price of the color printer.

According to the information given, Sarah can choose a printer that ranges in price from $170 to $300.

So, the compound inequality representing this problem is:
$170 ≤ x ≤ $300

To find out how much Sarah can plan to pay after the $35 rebate is deducted, we need to subtract $35 from the price range.

Therefore, the new compound inequality representing the price after the rebate is:
$135 ≤ x - $35 ≤ $265

Simplifying further:
$100 ≤ x ≤ $230

So Sarah can plan to pay between $100 and $230 after the rebate.

Part B:

Sarah's budget for the printer is $125.

To determine if she can stay within her budget, we compare it with the price range after the rebate:

$100 ≤ x ≤ $230

Since the lower limit of the price range after the rebate is $100, which is less than her budget of $125, she can stay within her budget and can choose a printer from the given range.

Answer 3

Part A: To form a compound inequality, we need to consider the price range of color printers that Sarah is looking for. The price range is from $170 to $300.

Let's represent the price of a color printer by the variable 'x'.
The compound inequality can be formed as follows:
170 ≤ x ≤ 300

To find out how much Sarah can plan to pay after the rebate, we need to subtract the rebate amount from the price range. The rebate amount is $35.

Thus, the new compound inequality becomes:
(170 - 35) ≤ x ≤ (300 - 35)
135 ≤ x ≤ 265

Therefore, Sarah can plan to pay between $135 and $265 after the rebate.

Part B: Sarah's budget is $125 for a printer. To check if she can stay within her budget, we need to see if her budget falls within the price range after the rebate.

The price range after the rebate is $135 to $265.

Since $125 is not within this range, Sarah cannot stay within her budget of $125 for the printer. She would need to increase her budget or choose a different printer that falls within her budget range.