The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the f

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The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the first. Find the numbers.

We have three numbers, x, y, and z.

1. x + y + z = 171
2. y = 1/2x
3. z = 3/4x

Substitute (2) and (3) into (1)
x + 1/2x + 3/4x = 171

Use a common denominator of 4 for each x term
4x/4 + 2x/4 + 3x/4 = 171
(4 + 2 + 3)x/4 = 171
9x/4 = 171

Plug this equation into our search engine, and we get x = 76
So y = 1/2(76) --> y = 38
Then z = 3/4(76) --> z = 57