Question

If a rectangular lot measures 160 ft. x 110 ft., and 15 foot set backs are required from each lot line, how much area is left? If 65 cars require 32,500 square feet, how many cars will the small rectangle hold?
There will be ______ square feet in the smaller lot.

The number of cars is____. (Use a whole number.)

Answer 1

Answer:

Part 1) There will be $10,400$ square feet in the smaller lot

Part 2) The number of cars is $20$

Step-by-step explanation:

Step 1

Find the area of the small rectangle

The area of rectangle is equal to

$A=LW$

we have that

$L=160-2*15=130\ ft$

$W=110-2*15=80\ ft$

$A=130*80=10,400\ ft^{2}$

Step 2

we know that

$65$ cars require $32,500$ square feet  

so

by proportion

Find how many cars will the small rectangle hold

$\frac{65}{32,500}=\frac{x}{10,400}\\ \\32,500*x=10,400*65\\ \\x=10,400*65/32,500\\ \\x=20.8\ cars\\ \\x=20\ cars$

Answer 2

$(160-2\times15)(110-2\times15)=130\times80=10400$
There will be 10400 square feet in the smaller lot.

$\frac{32500}{65} =500 \text{ square feet per car} \\ \\ \frac{10400}{500}= 20.8 \approx 20$
The number of cars is 20