SOLUTION: A photographer increases the side of a square in the ratio 4:5. By what percentage are the sides increased?

Question 1092588: A photographer increases the side of a square in the ratio 4:5. By what percentage are the sides increased?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the original length of the side of the square.
let y equal the new length of the side of the square.

you get x/y = 4/5

cross multiply to get 5x = 4y

solve for y to get y = 5x/4 = 5/4 * x

5/4 * x is equivalent to (4/4 + 1/4) * x which is equal to 1 * x + 1/4 * x.

the original length of the side is increased by 1/4 * the length of the original side.

that would be equal to 25% of the length of the original side.

another way of getting to the same answer is:

y = 5/4 * x = 1.25 * x

increase percent is equal to (1.25 * x - x) / x = .25.

multiply that by 100 to 25%.

assume the original length of the side is 100.

increase that by 25% and the length of the new side is 125.

the ratio of the original length to the new length is 100 / 125 which simplifies to 4/5 when you divide both numerator and denominator by 25.

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