SOLUTION: If x:y=7:4 and y:z=9:10, find the ratio x:y:z

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Question 1091916: If x:y=7:4 and y:z=9:10, find the ratio x:y:z
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x          y          z
7          4
           9         10


x          y          z
7          4        10(4/9)=40/9
           9         10

x:y:z
7%2A9 : 4%2A9 : %2840%2F9%29%2A9
63:36:40

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Ratios are like fractions. We like ratios in least terms,
so we want to see no common divisor for the pair in any ratio.
The pairs of numbers in each of the ratios given have no common divisor,
so for x, y and z to be integers, it should be a multiple of 4, and 9.
The smallest such number is 9%2A4=36
x:y=7:4=63:36 and y:z=9:10=36:40 gives us
x:y:z=highlight%28%2263%3A36%3A40%22%29

You could look at it as
y%2Fz=9%2F10 --> y=%289%2F10%29z
x%2Fy=7%2F4 --> x=%287%2F4%29z
system%28y=%289%2F10%29z%2Cx=%287%2F4%29z%29 --> system%28y=%289%2F10%29z%2Cx=%287%2F4%29%289%2F10%29z%29 --> system%28y=%289%2F10%29z%2Cx=%2863%2F40%29z%29 --> system%28y=%2836%2F40%29z%2Cx=%2863%2F40%29z%29