In 2 years a boy will be 3/4 as old as his sister. 2 years ago he was 2/3 as old as she. How old are they?

1 Answer
Sep 10, 2015

Answer:

The boy is #10#
and his sister is #14#

Explanation:

Define
#color(white)("XXX")b#: boy's current age
#color(white)("XXX")g#: his sister's current age

We are told
[1]#color(white)("XXX")b+2 = 3/4(g+2)#
and
[2]#color(white)("XXX")b-2= 2/3(g-2)#

[1] can be simplified into standard form as
[3]#color(white)("XXX")4b-3g=-2#

[2] can be simplified into standard form as
[4]#color(white)("XXX")3b-2g=2#

Multiply [3] by 2 and [4] by 3
[5]#color(white)("XXX")8b-6g=-4#
[6]#color(white)("XXX")9b-6g=6#

Subtract [5] from [6]
[7]#color(white)("XXX")b=10#

Substitute #10# for #b# in [3]
[8]#color(white)("XXX")4(10)-3g=-2#

[9]#color(white)("XXX")3g = 42#

[10]#color(white)("XXX")g=14#