SOLUTION: The sum of present ages of A and B is 7 times the difference of their ages. 5 years hence, their total ages will be 9 times the difference of their ages. What is the present age of

Question 990631: The sum of present ages of A and B is 7 times the difference of their ages. 5 years hence, their total ages will be 9 times the difference of their ages. What is the present age of elder one (in years)?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of present ages of A and B is 7 times the difference of their ages.
5 years hence, their total ages will be 9 times the difference of their ages.
What is the present age of elder one (in years)?
:
let a = A's present age
let b = B's age
:
Write an equation for each statement
:
"The sum of present ages of A and B is 7 times the difference of their ages."
a + b = 7(a-b)
a + b = 7a - 7b
b + 7b = 7a - a
8b = 6a
b = a
b = .75a
:
"5 years hence, their total ages will be 9 times the difference of their ages."
(their difference in their ages will never change)
a+5 + b+5 = 9(a - b)
a + b + 10 = 9a - 9b
b + 9b + 10 = 9a - a
10b + 10 = 8a
Replace b with .75a, from the 1st statement
10(.75a) + 10 = 8a
7.5a + 10 = 8a
10 = 8a - 7.5a
10 = .5a
a = 10/.5
a = 20 yrs old and he is the eldest
:
:
To check this find b's age
b = .75(20)
b = 15 yrs, 5 yrs younger than a
;
Check this in the 2nd statement
"5 years hence, their total ages will be 9 times the difference of their ages."
20+5 + 15+5 = 9(5)
25 + 20 = 45
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