sharon has some one dollar bills and some five dollar bills. She has 14 bills altogether. The value of the bills is 30. how many of each kind of bills does she have?

Answer 1

The key to this problem is understanding that is you have two five-dollar bills, then you have $10. If you have 3, then you have $15. If you have x five-dollar bills, then the value is represented by 5x.

Let x = #of five-dollar bills and y = # of one-dollar bills.

First equation:

x + y = 14 (because there is a total of 14 bills).

5x + 1y = 30 (5x as we have seen represents the value of x 5-dollar bills, and 1y represents the value of y one-dollar bills).

Probably the easiest way to solve this system is to subtract the 1st equation from the 2nd (which causes the variable y to disappear).

5x + y = 30

x + y = 14

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4x = 16

x = 4

So, y = 10.

5(4) + 1(10) = 20 + 10 = $30.

Note: If you wanted to use the substitution method instead, solve the 1st equation for y and substitute into the 2nd.

y = 14 - x

5x + (14 - x ) = 30

4x + 14 = 30

4x = 16

x = 4

y = 14 - 4 = 10