SOLUTION: The sum of three numbers is 200. The ratio of the first to the second is 5:6 and that of the second to the third is 2:3 What is the difference between the largest and the smallest

Question 756947: The sum of three numbers is 200. The ratio of the first to the second is 5:6 and that of the second to the third is 2:3
What is the difference between the largest and the smallest number?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let the three numbers be a,b,c
Sum: a + b + c = 200
Ratios: a/b = 5/6; b/c = 2/3 -> c/b = 3/2
Dividing the first equation by b gives:
a/b + 1 + c/b = 200/b
Substituting and solving for b gives:
5/6 + 1 + 3/2 = 200/b
20/6 = 200/b
b = 60
Therefore a = 5/6(60) = 50; c = 3/2(60) = 90
Ans: 50,60,90

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