Question 1196511
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I have no idea what tutor @josgarithmetic was doing to solve the problem; in any case, his answer does not satisfy the given conditions.<br>
Here are a few ways you can solve this kind of problem.<br>
(1) Choose any value for one variable and use the given ratios to find the corresponding values of the other two.  Then make a ratio of the three values, and convert the ratio to whole numbers if needed.<br>
y = 1 --> x=3/8; z = 3/7
the ratio x:y:z is (3/8):1:(3/7) = 21:56:24<br>
(2) Given 8x, 3y, and 7z all equal to the same number, let that number be the LCM of the three coefficients: 8*3*7 = 168.  Then
x = 168/8 = 21; y = 168/3 = 56; z = 168/7 = 24
and the ratio is again x:y:z = 21:56:24<br>
(3) Having observed how solution method (2) works, you should be able to see that the solution is simply
x:y:z = (3*7):(8*7):(8*3) = 21:56:24<br>