SOLUTION: Ann is four times as old as Ben and five times as old as Carrie. By the time Carrie is twice her age now, her age will be one third that of Ann. If Ben is three years older than Ca
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-> SOLUTION: Ann is four times as old as Ben and five times as old as Carrie. By the time Carrie is twice her age now, her age will be one third that of Ann. If Ben is three years older than Ca
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Question 963792: Ann is four times as old as Ben and five times as old as Carrie. By the time Carrie is twice her age now, her age will be one third that of Ann. If Ben is three years older than Carrie, how old is each one now? After how many years will be Carrie half as old as Ann? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! let a = Ann's present age
let b = Ben's
let c = Carrie's
:
Write an equation for each statement
:
Ann is four times as old as Ben
a = 4b
and five times as old as Carrie.
a = 5c
By the time Carrie is twice her age now, her age will be one third that of Ann.
2c = (a+c)
multiply both sides by 3
6c = a + c
replace a with 4b
6c = 4b + c
Replace b with (c+3); Ben is three years older than Carrie
6c = 4(c+3) + c
6c = 4c + 12 + c
6c - 5c = 12
c = 12 yrs is Carrie's age
then
12 + 3 = 15 yrs is Ben's age ("Ben is three years older than Carrie")
and
a = 4(15)
a = 60 yrs is Ann's age
:
how old is each one now?
Ann is 60
Ben is 15
Carrie is 12
:
After how many years will be Carrie half as old as Ann?
Let y = number of years for this to be true
c + y = (a+y)
c = 12, a = 60
12 + y = (60+y)
multiply both sides by 2
2(12+y) = 60 + y
24 + 2y = 60 + y
2y - y = 60 - 24
y = 36 yrs for Carrie to be half Ann's age
:
let's check that out
Ann: 60 + 36 = 96
Carrie: 12 + 36 = 48, half of 96
