SOLUTION: 8 years ago, Jimmy was three times as old as Anne. In 4 years, Jimmy will be 3/2 of Anne's age. How old is Jimmy now?

Question 155567: 8 years ago, Jimmy was three times as old as Anne. In 4 years, Jimmy will be 3/2 of Anne's age. How old is Jimmy now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let j = Jimmy's age now
Let a = Anne's age now
:
Write an equation for each statement:
"8 years ago, Jimmy was three times as old as Anne."
(j-8) = 3(a-8)
Smplify
j - 8 = 3a - 24
j = 3a - 24 + 8
j = (3a-16)
:
" In 4 years, Jimmy will be 3/2 of Anne's age."
j + 4 = (a+4)
Get rid of the denominator, multiply both sides by 2:
2(j+4) = 3(a+4)
2j + 8 = 3a + 12
2j = 3a + 12 - 8
2j = 3a + 4
:
How old is Jimmy now?
From the 1st equation, substitute (3a-16) for j in the above equation
2(3a-16) = 3a + 4
6a - 32 = 3a + 4
6a - 3a = 4 + 32
3a = 36
a =
a = 12 yrs is Anne's age now
then
j = 3(12) - 16 (from the 1st equation)
j = 36 - 16
j = 20 yrs is Jimmy's age now
:
:
Check our solution in the statement:
In 4 years, Jimmy will be 3/2 of Anne's age.
24 = * 16
24 = 24
:
How about this? It it make sense to you?
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