SOLUTION: Ann and Bill's age adds up to 91. Ann is now three times as old than what Bill was when Ann was two times older than him. How old is Ann and Bill?

Question 1080192: Ann and Bill's age adds up to 91. Ann is now three times as old than what Bill was when Ann was two times older than him. How old is Ann and Bill?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I could not get integer solutions to this unless their ages add up to 90, not 91
:
Ann and Bill's age adds up to 90.
a + b = 90
b = (90 - a)
Ann is now three times as older than what Bill was when Ann was two times older than him.
:
let y = no. of yrs ago that a was twice b's age
a - y = 2(b-y)
a - y = 2b - 2y
a - y + 2y = 2b
y = (2b - a); yrs ago when a was twice b
" Ann is now three times as older than what Bill was when Ann was two times older than him."
a = 3(b - (2b-a))
a = 3(b - 2b + a)
a = 3(-b + a)
a = -3b + 3a
3b = 3a - a
3b = 2a
replace b with (90-a)
3(90-a) = 2a
270 - 3a = 2a
270 = 5a
a = 270/5
a = 54 yrs old is Ann
then
b = 90 - 54
b = 36 yrs old is Bill
:
:
See if this checks out, find y
y = 2b - a
y = 72 - 54
y = 18 yrs ago a was twice b
"Ann is now three times as old than what Bill was when Ann was two times older than him."
54 = 3(36 - 18); (18yrs ago a=36 and b=18)
54 = 3(18)

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