an old picture has dimensions 33 inches by 24 inches. what one length must be cut from each dimension so that the ratio of the shorter side to the longer side is 3/4

Answer 1

new long side = 33-x
new short side = 24-x

(24-x)/(33-x) = 3/4

cross-multiply and solve for x

Answer 2

how do i cross multiple whole number

Answer 3

3(33-x) = 4(24-x)
99 - 3x = 96 - 4x
x = -3

At this point we realize that we actually have to increase each dimension by 3 inches to achieve the 3/4 ratio
new long side = 36
new short side = 27

27/36 = 3/4

(analysis: the original ratio is 24/33 = 7272..

by subtracting the same number from both numerator and denominator the ration gets smaller,

e.g. 23/32 = .71875
22/31 = .7096

so we have to ADD the same number to both top and bottom to get a larger ratio.)

Answer 4

9

Answer 5

If you want the ratio of the shorter side to the longer side to be 3/4, you actually need to ADD 9 inches to each dimension.

new long side = 33 + 9 = 42 inches
new short side = 24 + 9 = 33 inches

33/42 = 3/4

Therefore, to achieve the desired ratio, you need to cut 9 inches off each dimension.