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The number that must be added to each term of the ratio $9 : 16$ to make the ratio $2 : 3$ is ____.

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Detailed Solution

The number that must be added to each term of the ratio 9:16 to make the ratio 2:3 is 5.
It is given that, the ratio

9 : 16

becomes

2 : 3

when added with some number.
Let

x

be the required number.

9 + x : 16 + x = 2 : 3

9 + x 16 + x = 23

By cross-multiplication, we get,

27 + 3 x = 32 + 2 x

By solving the above equation,
3x-2x = 32-27
x = 5
Hence the number is

5

.
Hence, the required answer is 5.

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