Question

6. A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the area of the field by

20%. He will do this by increasing the length and width by the same amount, x. Which equation represents the
area of the new field?
A. (100 + 2x)(150 + x) = 18,000
B. 2(100+ x) + 2(150 + x) = 15,000
C. (100+ x)(150 + x) = 18,000
D. (100 + x)(150 + x) = 15,000

Answer 1

C

Explanation:

First, we find the area of the field with the original measurements.

100 x 150 = 15,000

That number will be increased by 20%, so multiply it by 1.2

15,000 x 1.2 = 18,000

This means the equation will have to equal 18,000

This eliminates choices B and C

Both the length and width are increased by the same amount, making A not the right choice since there is a 2x. This 2x means that one of the sides is being doubled increased than the other side, so that would make it to where both sides are not increased equally.

This leaves us with choice C where it equals 18,000 and both sides are increased by an equal amount.