SOLUTION: Three numbers are in the ratio of 4:5:6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers

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Question 1106200: Three numbers are in the ratio of 4:5:6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
As posted, I interpret "the third" to mean the third number in a list of numbers,
where the first, second, and third are in the ratio 4:5:6 respectively.
That will not yield 3 integers, but fractions are numbers too.

Let the numbers be 4x , 5x , and 6x .
That makes sure that they are in the ratio of 4:5:6.
6x%2B4x=10x is the sum of the largest and the smallest.
6x%2B55 is the sum of the third and 55.
So, the equation to solve is
10x=6x%2B55
10x-6x=55
4x=highlight%2855%29 is the smallest number
From 4x=55 we get
x=55%2F4
5x=5%2855%2F4%29=highlight%28275%2F4%29 , and
6x=6%2855%2F4%29=6%2A55%2F4=3%2A55%2F2=highlight%28165%2F4%29 .