translate the English into math.
<A square mirror has sides measuring 2 ft. less than the sides of a square painting>
let the sides of the square painting be x ft.
Then the sides of the mirror are each x-2 ft.
area of mirror = (x-2)(x-2)
area of painting = (x)(x)
<the difference in their areas is 32 ft^2
----> x^2 - (x-2)^2 = 32
x^2 - (x^2 - 4x + 4 = 32
x^2 - x^2 + 4x - 4 = 32
4x = 36
x = 9
old width : x
old length : x+3
old area : x(x+3)
new length : 2(x+3)
new width : x+3 - 1 or x+2
new area : 2(x+3)(x+2)
<area is increased by 150 in^s> or
the difference in their areas is 150
2(x+3)(x+2) - x(x+3) = 150
Can you take it from there?
Let me know what you got.
new width should be x-1
new area should be 2(x+3)(x-1)
equation should be
2(x+3)(x-1) - x(x+3) = 150
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