SOLUTION: In 2 years, a boy will be � as old as his sister. 2 years ago, he was 2/3 as old as she. How old is the boy now?

Question 487611: In 2 years, a boy will be � as old as his sister. 2 years ago, he was 2/3 as old as she. How old is the boy now?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=boy's age now
And let y=sister's age now
We are told that:
x+2=(3/4)(y+2) ---------------------eq1
We are also told that:
x-2=(2/3)(y-2)----------------------eq2
simplifying eq1, we get:
x+2=(3/4)y+6/4 multiply each term by 4:
4x+8=3y+6
or 4x-3y=-2------------------------------------eq1a
Now we simplify eq2:
x-2=(2/3)y-4/3 multiply each term by 3:
3x-6=2y-4
3x-2y=2--------------------------------------eq2a
Next, we multiply each term in eq1a by 2 and each term in eq2a by 3:
8x-6y=-4----eq1b
9x-6y=6------eq2b
subtract eq1b from eq2b:
x=10--------------------------------boy's age now
substitute x=10 into eq 1a:
40-3y=-2
-3y=-42
y=14----sister's age now
CK
10+2=(3/4)(14+2)
12=12
and
10-2=(2/3)(14-2)
8=8
Hope this helps---ptaylor

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