A rectangular field is 4 times as long as it is wide. If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. Find the dimensions of the original field. The original dimensions are feet long by feet wide.

L = 4W [A rectangular field is 4 times as long as it is wide.]

2 (L-10) + 2 (W+2) = 80 [If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. ]

Distributed: (2L - 20) + (2W + 4) = 80

Substitute the known value of L from the first equation into the second.

8W - 20 + 2W + 4 = 80

10 W - 16 = 80

Add 16 to each side

10W = 96

Divide each side by 10

W = 9.6 <<--original dimension

L = 9.6 * 4 = 38.4 <<--original dimension

...

If the length (38.4) is decreased by 10 feet (which would make it 28.4) and the width (9.6) is increased by 2 feet (11.6), the perimeter will be 80 feet.

28.4 + 28.4 + 11.6 + 11.6 = 80 feet.

Have a nice day : D