Question 994595: A is three as old as B, C is half as old as D and 8 years older than B. In ten years the sum of their ages will be 113. Find the ages of each.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! From the information provided, we have 4 equations in 4 unknowns:
A = 3B
D = 2C
C = B + 8
A + B + C + D + 40 = 113 [they will have each aged 10 years, so this adds 40 to the sum]
Solve for one of the variables in the last equation for the other three.
For example, D = 73 - A - B - C
Substituting D = 2C, we have 2C = 73 - A - B - C -> 3C = 73 - A - B
Since C = B + 8, we can write 3(B+8) = 73 - A - B
But A = 3B, so we now have an equation in one variable, B:
3(B+8) = 73 - 3B - B
This gives 7B = 49, or B = 7
You can now use the equations above to solve for the other variables.
Ans: A=21, B=7, C=15, D=30
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