Keith's
Pocket
Problem: Steve gave Keith an
amount of money equal to the amount in Keith's pocket. Keith then
gave Steve an amount of money equal to what Steve had left. Keith
then had $14 and Steve had $8. How much money did Keith originally
have in his pocket?
Solution: First, I let
S = the initial amount
of money for Steve & K = the initial amount of money for Keith.
Now let's go statement by statement:
Steve gave Keith an amount
of money equal to the amount in Keith's pocket.
S - K = X
Steve subtracted Keith's
amount from his own amount. Steve's remaining amount is now X.
Also, Keith now has double his initial amount (2K).
Keith then gave Steve an
amount of money equal to what Steve had left.
2K - X = Y
Keith's remaining amount
is now Y. Also, Steve now has double his previous amount,
which is now 2X.
Keith then had $14
Y = 14
... and Steve had $8.
2X = 8
How much money did Keith
originally have in his pocket?
We know that Y =
14. By solving for X, we know that X = 4. Lets
use the equation, 2K - X = Y to find Keith's initial amount,
K.
2K - 4 = 14
2K = 18
K = 9
We have found that
Keith originally had $9 in his pocket.
Extension: How much money did
Steve have originally in his pocket?
We can find Steve's
initial amount by substituting K=9 into the beginning equation,
S - K = X.
S - 9 = 4
S = 13
Therefore, Steve originally
had $13 in his pocket.
Reference: Project
INTERMATH
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