Answer:
15 : 20 : 8
Step-by-step explanation:
Given ratios a:b = 3:4 and b:c = 5:2, you want the ratio a:b:c in simplest form.
The extended ratio you want can be written only when the number of ratio units associated with 'b' is the same in both ratios. Multiplying the first ratio by 5, we get ...
a:b = 3:4 = 15:20
Multiplying the second ratio by 4 gives ...
b:c = 5:2 = 20:8
Now, 20 "ratio units" represent 'b' in both ratios, so we can combine them:
a:b:c = 15:20:8
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Additional comment
The value we chose to represent 'b' is the least common multiple (LCM) of the values that represent 'b' in the given (reduced) ratios.