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 much can she plan to pay after the rebate?

Question

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 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 with in her budget of $125 for the printer? Why or why not?

Answer 1

Part A:

Let x be the price of the color printer.
According to the problem, Office Max is offering a $35 rebate on all color printers.
After the rebate, the price Sara will have to pay is x - $35.

Since Sara is looking at color printers that range in price from $170 to $300, we can form the compound inequality:

170 ≤ x ≤ 300

To find out how much she can plan to pay after the rebate, we substitute the upper and lower bounds of x in the expression x - $35:

For x = 170, Sara will have to pay 170 - $35 = $135 after the rebate.
For x = 300, Sara will have to pay 300 - $35 = $265 after the rebate.

So, Sara can plan to pay after the rebate an amount between $135 and $265.

Part B:

Sara's budget for the printer is $125.

Since the amount Sara can plan to pay after the rebate ranges from $135 to $265, which is above her budget of $125, she cannot stay within her budget for the printer.

Answer 2

Part A:

Let's assume the price of the color printer that Sara chooses as "x".

According to the information given, the printers range in price from $170 to $300. We can write this as an inequality:

170 ≤ x ≤ 300

Since Sara is eligible for a $35 rebate, the price she will pay after the rebate can be represented as:

x - 35

So, the compound inequality for the problem would be:
170 ≤ x ≤ 300
x - 35

Now let's solve this compound inequality:

From the inequality 170 ≤ x ≤ 300, we can see that the largest value Sara can pay for the printer is 300.

Therefore, after the $35 rebate, the most she would pay is:
300 - 35 = $265

So, she can plan to pay a maximum of $265 after the rebate.

Part B:

Sara's budget for the printer is $125. Since the most she would pay after the rebate is $265, we can compare these values:

125 ≤ 265

Sara's budget is within the range of the maximum amount she would pay after the rebate. Therefore, she can stay within her budget of $125 for the printer.

Answer 3

Part A:

To find out how much Sara can expect to pay after the rebate, we need to subtract the rebate amount from the price of the color printer she chooses.

Let's represent the price of the color printer as "p" and the rebate amount as "$35". We can form a compound inequality as follows:

170 ≤ p ≤ 300

This inequality represents that the price of the color printer should be between $170 and $300 (inclusive), as Sara is looking at printers in this price range.

To determine how much Sara can expect to pay after the rebate, we need to subtract $35 from both sides of the inequality:

170 - 35 ≤ p - 35 ≤ 300 - 35

135 ≤ p - 35 ≤ 265

Therefore, Sara can expect to pay any amount between $135 and $265 after the rebate, depending on the printer she chooses.

Part B:
Sara's budget for the printer is $125. Since her budget is lower than the minimum price of the printer ($170), she cannot stay within her budget and purchase any color printer in the given price range. Therefore, she cannot stay within her budget of $125 for the printer.