SOLUTION: 3 years ago A's age was double of B. 7years later the sum of their united ages will be 83 years. Today the age of A is....????

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Question 919024: 3 years ago A's age was double of B.
7years later the sum of their united ages will be 83 years.
Today the age of A is....????
Answer by MathLover1(20850) About Me  (Show Source):
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3 years ago A's age was double of B.
A-3=2%28B-3%29.........eq.1
7 years later the sum of their united ages will be 83 years.
%28A%2B7%29%2B%28B%2B3%29=83.........eq.2
solve the system:
A-3=2%28B-3%29.........eq.1
%28A%2B7%29%2B%28B%2B7%29=83.........eq.2
___________________________
A-3=2%28B-3%29.........eq.1 solve for A
A=2%28B-3%29%2B3.......substitute in eq.2

%282%28B-3%29%2B3%2B7%29%2B%28B%2B7%29=83.........eq.2..solve for B
2B-6%2B3%2B7%2BB%2B7=83
3B%2B11=83
3B=83-11
3B=72
B=72%2F3
B=24
find A=2%28B-3%29%2B3
A=2%2824-3%29%2B3
A=2%2821%29%2B3
A=42%2B3
A=45
check:
3 years ago A's age was 45-3=42
3 years ago B's age was 24-3=21

42 is double of 21-true

7 years later the sum of their united ages will be 83 years.

A=45 7 years later will be A=45%2B7=52
B=24 7 years later will be B=24%2B7=31
and A%2BB=52%2B31=83-true