In the movie "Perfect Score" (Paramount 2004), the following SAT problem appears:
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"A ten quart mixture consists by volume of one
part juice and 9 parts water. If x quarts of
juice and y quarts of water are added to this
mixture to make a 27 quart mixture that consists
by volume of one part juice to two parts water, what
is the value of x? "
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The problem already gave the variables x=quarts of juice
and y =quarts of water which are added.
After adding we have 1+x juice and 9+y water.
One part of the problem tells that the sum 10+x+y is 27.
The second part of the problem is that 1/3 of it is water
which means (10+x+y)/(1+x) = 3. Formally this is a system
of linear equations
10+x+y = 27
3(1+x) = 10+x+y
with solution x=8 and y=9.
Tis can of course also be solved quickly from knowing that
the total amount is 27 and a third of it is 1+x. So that 1+x=9
or x=8. The variable y is not needed in this short cut at all.
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