document.write( "Question 1151939: an art museum sold 63 tickets in 30 minutes. The ratio of adult to child tickets was 5:1. The ratio of adult to senior tickets was 5:3. How many of each kind of ticket were sold? \n" ); document.write( "

Algebra.Com's Answer #773834 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The formal algebraic solutions by tutors @MathTherapy and @MathLover1 using ratios are valid, but a lot more work than necessary.

\n" ); document.write( "The mental solution by tutor @ikleyn is by far the easiest way to solve the problem.

\n" ); document.write( "If you want to formalize her solution, you get an algebraic solution with much less work than the other algebraic solutions you have seen.

\n" ); document.write( "adult:senior= 5:3 and adult:child = 5:1 means adult:senior:child = 5:3:1

\n" ); document.write( "So let the numbers of tickets be
\n" ); document.write( "5x = adults
\n" ); document.write( "3x = seniors
\n" ); document.write( "x = children

\n" ); document.write( "The total number of tickets was 63:

\n" ); document.write( " $\"5x%2B3x%2Bx+=+63\"$
\n" ); document.write( " $\"9x+=+63\"$
\n" ); document.write( " $\"x+=+7\"$

\n" ); document.write( "The numbers of tickets were
\n" ); document.write( "adults = 5x = 35
\n" ); document.write( "seniors = 3x = 21
\n" ); document.write( "children = x = 7

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