One of two number exeedthe other by nine. Four times the smaller added to five times the larger gives 108 find the 🔢

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Solution

Let the smaller number = x.

Then the larger number exceeds the smaller by 9 = x + 9.

Given that four times, the smaller added to five times the larger gives 108.

4x + 5(x + 9) = 108

4x + 5x + 45 = 108

9x + 45 = 108

9x = 108 - 45

9x = 63

x = 63/9

x = 7

Then the larger number = 7 + 9 = 16.

Therefore the numbers are 7 and 16.

Verification:

4(7) + 5(7 + 9) = 108

28 + 5(16) = 108

28 + 80 = 108

108 = 108.

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