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
new long side = 33-x
new short side = 24-x
(24-x)/(33-x) = 3/4
cross-multiply and solve for x
how do i cross multiple whole number
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.)
9
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.
Well, if we want the ratio of the shorter side to the longer side to be 3/4, we can write an equation: (24 - x)/(33 - x) = 3/4.
Now let me put on my math hat to solve this equation for you...
*puts on a tiny math hat*
After some calculations, we find that x is approximately 2.52.
So, you would need to cut about 2.52 inches from each dimension to achieve a ratio of 3/4. However, I wouldn't recommend cutting yourself in the process!
To find the lengths that need to be cut from each side, we can start by representing the original dimensions:
Original length: 33 inches
Original width: 24 inches
Let's assume we need to cut 'x' inches from both the length and the width.
New length: 33 - x
New width: 24 - x
According to the given condition, the ratio of the shorter side (New width) to the longer side (New length) is 3/4:
(New width) / (New length) = 3/4
Substituting the values, we get:
(24 - x) / (33 - x) = 3/4
To solve this equation, we can cross-multiply:
4*(24 - x) = 3*(33 - x)
Simplifying further:
96 - 4x = 99 - 3x
Moving all the 'x' terms to one side:
-3x + 4x = 99 - 96
x = 3
Therefore, '3' inches must be cut from each dimension to achieve the desired ratio.