Question

Mick recently had new carpet installed. the cost of the carpet including installation was $8.14 per square foot before any discounts. the rectangular room he had carpeted measured 24 feet long and 18 feet wide. if mick actually paid $3,235.16, what discount percentage did he receive? assume there are no taxes.

Answer 1

8%

Explanation:

Let’s first determine the cost before any discount.

To do so, we first need to determine the area to be carpeted:

Area of Rectangle = Length × Width = 24 ft × 18 ft = 432 square feet.

To find the cost before discount we need to multiply the area by the cost per square foot:

Cost Before Discount = Area × Cost per square foot

Cost Before Discount = 432 square feet × $8.14 per square foot

Cost Before Discount = $3,516.48

We can now determine the discount percentage he received:

Cost After Discount = Cost Before Discount − (Discount % × Cost Before Disc.)

$3,235.16 = $3,516.48 – (Discount % × $3,516.48)

To solve, it is easiest to plug in each answer to see which discount percentage is the correct solution (i.e. “work backwards” from the given answers) or use the equation solver on our calculator.

We find that a discount of 8% is the correct solution.

If you instead prefer to use algebra to solve for the discount percentage, here are the steps.

We will rewrite the equation, using x to represent “Discount %”.

$3,235.16 = $3,516.48 − (x × $3,516.48)

$3,235.16 = $3,516.48 − $3,516.48x

Factoring out $3,516.48 we have:

$3,235.16 = $3,516.48(1 − x)

Note: Once you get comfortable with this type of problem you should skip straight to the step above.

Dividing both sides by $3,516.48 we have:

$3,235.16$3,516.48=1−x

0.92 = 1 − x

x = 0.08 = 8%