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shared by tylerdesi34 on 23 Dec 14 - Cached

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
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Many problems lend themselves to being solved with systems of linear equations. In "real life", these problems can be incredibly complex. This is one reason why linear algebra (the study of linear systems and related concepts) is its own branch of mathematics. In your studies, however, you should generally be faced with much simpler problems. What follows are some typical examples.
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Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:
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The new number will have the values of the digits (represented by the variables) in reverse order: new number: 10u + 1t And this new number is twenty-seven more than the original number: (new number) is (old number) increased by (twenty-seven) 10u + 1t = 10t + 1u + 27
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u + t = 7 u – t = 3
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