Question 22774: I am a parent trying to help my son figure out how to solve the following:
Bill is twice as old as his brother Dan. In 7 years Bill will be only one and one half as old as Dan. How old is Bill now?
I would like the details on solving so I can teach him properly.
Thank you.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! First define the things you are asked for:
Let Bill be x years NOW
Let Dan be y years NOW.
so, we know x = 2y --eqn1
Also, in 7 years time, Bill will be x+7 and Dan will be y+7. At this point, (x+7) = (3/2)(y+7) --eqn2
eqn2 simplifies to 2x+14 = 3y+21
--> 2x - 3y = 7
Now, from eqn1, x = 2y, so sub this into the above version of eqn2, which becomes: 2(2y) - 3y = 7, which becomes
4y - 3y = 7
y = 7
Hence x=2(7) --> x=14
So, Bill is 14 years old now.
check:
in 7 years, we have ages 14 and 21, where 21 is "one and one-half" as much as 14.
Hope this is clear.
jon.
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