SOLUTION: 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.

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
RELATED QUESTIONS
John is twice as old as Peter. In 8 years, John�s age will be 2 more than the sum of... (answered by Edwin McCravy)

C's age is 6 more than the sum of the ages of A and B. Five years from now A will be half (answered by ankor@dixie-net.com)

John is as old as Cindy will be when John is twice as old as Cindy was when John was half (answered by Edwin McCravy)

the sum of A and B is 30 years and 5 years hence A will be three times as old as B. Find... (answered by stanbon)

Mark is 8 years younger than Gerry. In ten years, he will be ten years more than one-half (answered by stanbon)

Carol is three times as old as John who is ten years older than Henry. The sum of their... (answered by ikleyn,Timnewman)

Woodstock is currently ten years older than his friend Snoopy. In three years, Woodstock... (answered by richwmiller)

T is older than G, and the difference of their ages is 40. If forty years ago T was half... (answered by ankor@dixie-net.com)

A is half as old as b and b is half as old as c.the sum of their ages is 105 years... (answered by MathLover1)