Example 1

Enid has a stack of five-dollar bills and ten-dollar bills. She has 22 bills altogether, and the pile is worth $190. How many bills of each type does Enid have?

Write a system of equations to represent this scenario (Modelling).

The statements "Let F be..." and "let T be..." are used to define the variables F and T. This is an important step in modelling because it makes the meaning of each variable clear for the reader.

Let F be the number of five dollar bills and let T be the number of ten dollar bills.

There are 22 bills altogether, so F + T = 22. The total value of the five dollar bills is 5 F and the total value of the 10 dollar bills is 10 T . The total value of all of the bills combined is $190, so 5F + 10 T = 190.

Solve the system of equations (Analysis).

Choose a method appropriate for the system. Substitution is shown here.

How many of each type of bill does Enid have (Interpretation)?

Enid has 16 ten-dollar bills and 6 five-dollar bills.

Does the conclusion agree with the original information? (Was the problem solved?)

Yes. There are a total of 22 bills and their total value is 5(6) + 10(16) = 190 dollars.