Question 963792
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 = {{{1/3}}}(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 = {{{1/2}}}(a+y)
c = 12, a = 60
12 + y = {{{1/2}}}(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