Exercise 26 Page 440

If Mrs. Albright should purchase the rugs, the total area of the circular rugs has to cover at least 80 % of the floor. Rug's area/Floor's area≥ 80 % Let's illustrate the floor and the number of rugs Mrs. Albright can put on the floor.

We see that 20 rugs will fit in the space without overlapping. Since the floor is a rectangle, its area is the product of its width and length.

A=wl

SubstituteII

w= 20, l= 25

A=( 20)( 25)

Multiply

Multiply

A=500

The area of the floor is 500 feet^2. Next, we will calculate the area of the rugs. The rugs have a diameter of 5 feet, which means they have a radius of 2.5 feet. Now we can calculate the area of one rug and finally the area of all 20 rugs if we multiply this number by 20.

A=π r^2

Substitute

r= 2.5

A=π( 2.5)^2

▼

Evaluate right-hand side

CalcPow

Calculate power

A=π(6.25)

CommutativePropMult

Commutative Property of Multiplication

A=6.25π

MultEqn

LHS * 20=RHS* 20

20A=125π

Finally, we will divide the area of the rugs by the area of the floor. 125π/500≈ 0.79 The rugs cover only 79 % of the floor. Therefore, she should not buy the rugs.