SOLUTION: express 100 as the sum of two numbers for which the ratio of one number, increased by 5, to the other number, decreased by 5, is 4

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Question 719957: express 100 as the sum of two numbers for which the ratio of one number, increased by 5, to the other number, decreased by 5, is 4
Answer by graphmatics(170) About Me  (Show Source):
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Here we go. Let's let x be the larger of the two numbers. For now we'll let t be the amount we can subtract from x to get the smaller of the 2 numbers. So
x%2B%28x-t%29=100
2%2Ax-t=100
x=%28100%2Bt%29%2F2
We next just put the ratio sentence into an equation we get
%28x%2B5%29%2F%28x-t-5%29=4
Well we know what x is in terms of t so we substitute that and get
%28%28100%2Bt%29%2F2%2B5%29%2F%28%28100%2Bt%29%2F2-t-5%29=4
50%2Bt%2F2%2B5=4%2A%2850%2Bt%2F2-t-5%29
50%2Bt%2F2%2B5=200%2B2t-4t-20
t%2F2-2t%2B4t=200-20-50-5
t%2F2%2B4t%2F2=125
5t%2F2=125
5t=250
t=50
so x=%28100%2B50%29%2F2=75

If the large number is 75 we easily get the small number is 25. The two numbers clearly work.(80/20=4).