Officer 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

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

Answer 1

Part A:

Let x represent the price of the printer.

The compound inequality representing this problem is:
170 ≤ x ≤ 300.

To calculate the final price, we subtract the rebate from the price of the printer:
x - 35 = final price.

To find a specific value for the final price, we can substitute the minimum and maximum values of the price range into the equation:
170 - 35 = 135
300 - 35 = 265

Therefore, Sara can expect to pay anywhere between $135 and $265 after the rebate.

Part B:

Sara's budget is $125.
Since $125 is less than the minimum possible price after the rebate ($135), Sara cannot stay within her budget of $125 for the printer.

Answer 2

Part A:

Let's represent the price range of the color printers as follows:

170 ≤ x ≤ 300

Where x represents the price of the printer.

To calculate how much Sara can plan to pay after the rebate, we subtract the rebate amount of $35 from the price range:

170 - 35 ≤ x - 35 ≤ 300 - 35

Simplifying, we get:

135 ≤ x - 35 ≤ 265

Further simplifying:

135 + 35 ≤ x ≤ 265 + 35

170 ≤ x ≤ 300

So, Sara can expect to pay between $170 and $300 after the rebate.

Part B:
Sara's budget for the printer is $125. From Part A, we know that the price of the color printer range is between $170 and $300 after the rebate. Therefore, Sara cannot stay within her budget of $125 because the lowest price after the rebate is $170, which is greater than her budget.

Answer 3

Part A: Forming the compound inequality and solving:

Let's use the variable "x" to represent the price of the color printer.

The problem states that Officer Max is offering a $35 rebate on all color printers. This means that Sara can subtract $35 from the original price of the printer to determine the final price after the rebate.

So, the compound inequality representing this problem is:
$170 ≤ x - $35 ≤ $300

To solve this compound inequality, we'll separate it into two separate inequalities:

The first inequality:
$170 ≤ x - $35

Adding $35 to both sides of the inequality:
$170 + $35 ≤ x

Simplifying:
$205 ≤ x

The second inequality:
x - $35 ≤ $300

Adding $35 to both sides of the inequality:
x ≤ $300 + $35

Simplifying:
x ≤ $335

So the compound inequality is:
$205 ≤ x ≤ $335

Part B: Checking whether Sara's budget of $125 is sufficient:

Sara's budget for the printer is $125. To determine if this amount is within her budget, we need to check if her budget falls within the range of prices after the rebate.

From Part A, we found that the range of prices after the rebate is $205 ≤ x ≤ $335.

Comparing Sara's budget of $125 with the range of prices after the rebate:
$205 ≤ $125 ≤ $335

Since $125 is not within the range of $205 to $335, Sara cannot stay within her budget of $125 for the printer.