Question

Sarah used a scale of ½ inch = 3 feet for a drawing of her business. On the drawing, a rectangular room measures 2 ½ inches by 3 ¾ inches. Sarah wants to purchase new carpet for the room that costs $3.79 per square foot. Before sales tax, how much will the new carpet cost? Round to the nearest cent.

Answer 1

Answer:

The new carpet will cost $1279.13 to the nearest cent

Step-by-step explanation:

The given is:

1. Sarah used a scale of $\frac{1}{2}$ inch = 3 feet

2. On the drawing, a rectangular room measures $2\frac{1}{2}$ inches

     by $3\frac{3}{4}$ inches

3. Sarah wants to purchase new carpet for the room that costs $3.79

    per square foot

We need to find much the new carpet will cost

∵ The scale is 0.5 inch = 3 feet

∵ The dimensions of the room on the drawing are $2\frac{1}{2}$ inches and

    $3\frac{3}{4}$ inches

∵ $2\frac{1}{2}$ = 2.5

∵ $3\frac{3}{4}$ = 3.75

Use the ratio method

→  inches  :  feet

→  0.5        :  3

→  2.5        :  x

→  3.75      :  y

- By using cross multiplication

∴ 0.5 x = 2.5 × 3

∴ 0.5 x = 7.5

- Divide both sides by 0.5

∴ x = 15 feet

∴ 0.5 y = 3.75 × 3

∴ 0.5 y = 11.25

- Divide both sides by 0.5

∴ y =  22.5 feet

∴ The actual dimensions of the room are 15 feet and 22.5 feet

Now lets find the area of the room which is the area of the carpet

∵ Area of the carpet = 15 × 22.5

∴ Area of the carpet = 337.5 feet²

∵ The cost of the carpet is $3.79 per square feet

∴ The cost of the carpet = 3.79 × 337.5 = 1278.125

∴ The cost of the carpet = $1279.13 to the nearest cent

The new carpet will cost $1279.13 to the nearest cent

Learn more:

You can learn more about ratio in brainly.com/question/13076219

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