SOLUTION: A copying machine can make copies that are 80%, 100% and 150% as large as the original. By making copies of copies, what is the smallest number of times you must use the machine

Question 257423: A copying machine can make copies that are 80%, 100% and 150% as large as the
original. By making copies of copies, what is the smallest number of times you
must use the machine if you want a copy of an original that is 324% as large as
the original?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
A copying machine can make copies that are 80%, 100% and 150% as large as the
original. By making copies of copies, what is the smallest number of times you
must use the machine if you want a copy of an original that is 324% as large as
the original?


Let x = the integer which is the number of times to use the
80% setting and y = the integer which is the number of times
to use the 150% setting:

Then changing the percents to decimals:



Change the decimals to the fractions

,  and  



Write  as ,  as , and  as 







Cross-multiply:



Divide both sides by the right side





All those exponents must be 0, since they are integers,
so



Solve that and get ,

So we use the 80% copier 2 times and the 150% copier 4 times.

Edwin

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