Question 69978

Let x=his sister's age now
x-3=sister's age 3 years ago
x-2=sister's age 2 years ago
x-1=sister's age 1 year ago
7(x-3)=boy's age 3 years ago
4(x-2)=boy's age 2 years ago
3(x-1)=boy's age 1 year ago
(2.5)x=boy's age now

Now we know that if we add 1 year to the boy's age three years ago, then we'll have his age two years ago and so forth.  There's several equations that will yield the correct answer.  Lets do the 3 year one.  You can do the others for drill:

7(x-3)+1=4(x-2) get rid of parens
7x-21+1=4x-8  or
7x-20=4x-8  add 20 to and subtract 4x from both sides
7x-4x=20-8
3x=12
x=4 years old ----------------------sister's age now

2.5x=2.5*4=10 years old---------------- boy's age now

CK
Boy's age 1 year ago:  3(x-1)=3*4-3=9;  10-1=9
Boy's age 2 years ago: 4(x-2)=4*4-8=8;  10-2=8
Boy's age 3 years ago: 7(x-3)=7*4-21=7;  10-3=7


Hope this helps----ptaylor