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 [tex]\frac{1}{2}[/tex] inch = 3 feet
2. On the drawing, a rectangular room measures [tex]2\frac{1}{2}[/tex] inches
   by [tex]3\frac{3}{4}[/tex] 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 [tex]2\frac{1}{2}[/tex] inches and
  [tex]3\frac{3}{4}[/tex] inches
∵ [tex]2\frac{1}{2}[/tex] = 2.5
∵ [tex]3\frac{3}{4}[/tex] = 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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