I just wrote an exam in Math and this question puzzled me. I hit a dead-end. Here it is:

If a field is enlarged by making it 10 feet longer and 5 feet wider, its area is increased by 1050 square feet. If its length is decreased by 5 feet and its width is decreased by 10 feet, its area is decreased by 1050 square feet. What are the original dimensions of the field?

Any help would be awesome... I already wrote the exam so I just want to be able to know the correct way to solve it.

set up a system of equations !

let x = the original length
let y = the original width

then original area = xy [square units]

If a field is enlarged by making it 10 feet longer and 5 feet wider, its area is increased by 1050 square feet

(x +10)(y + 5) = xy + 1050

If its length is decreased by 5 feet and its width is decreased by 10 feet, its area is decreased by 1050 square feet.

(x - 5)(y - 10) = xy - 1050

expand and solve the system...try !

¶

L * W = A
(L + 10)(W + 5) = A + 1050
(L - 5)(W - 10) = A - 1050

LW + 5L + 10W + 50 = LW + 1050
LW - 10L - 5W + 50 = LW - 1050

L + 2W = 200
-2L - W = -220

2L + 4W = 400
-2L - W = -220
3W = 180
W = 60 ft
L = 200 - 120 = 80 ft

there is no solution that I can find