Rachel has an 80:1 scale drawing of the floor plan of her house. On the floor plan, the dimensions of her rectangular living room are 1 7/8 by 2 1/2 inches. What is the area of her actual living room in square feet?

208⅓ ft²

Step-by-step explanation:

The dimensions of Rachel's living room are 80 times the measurements on the scale drawing.

Calculate the width:

w = 80 * 1⅞

Convert the mixed number to an improper fraction = 80 * 15/8

Cancel the 8s = 10 * 15

= 150 in

Convert inches to feet = 150/12

Convert the improper fraction to a mixed number = (144 + 6) / 12

= 12⁶/₁₂

Reduce the fraction to lowest terms = 12½ ft

Calculate the length

l = 80 * 2½ = 80 * 5/2 = 40 * 5 = 200 in = 200/12 = (192 + 8) / 12

l = 16⁸/₁₂ = 16⅔ ft

Calculate the area

A = lw

A = 16⅔ * 12½

Convert the mixed numbers to improper fractions

A = 50/3 * 25/2

Cancel the 2s

= 25/3 * 25

Multiply numerators and denominators

= 625/3

Convert the improper fraction to a mixed number

= (624 + 1) / 3

= 208⅓ ft²

The area of Rachel's living room is 208⅓ ft².