Sharon has some one-dollar bills and some five-dollar bills. She has fourteen bills. The value of the bills is $30.00. Solve a system of equations using elimination to find how many of each kind of bill she has.
Let x be the number of one-dollar bills and y be the number of five-dollar bills.
We can set up the following system of equations based on the given information:
x + y = 14 (equation 1: the number of bills)
1x + 5y = 30 (equation 2: the value of the bills in dollars)
To solve this system using elimination method, let's multiply equation 1 by 5:
5x + 5y = 70 (equation 3)
Now we can subtract equation 3 from equation 2 to eliminate the y variable:
1x + 5y - (5x + 5y) = 30 - 70
x - 5x = -40
-4x = -40
Dividing both sides of the equation by -4, we get:
x = 10
Substituting the value of x into equation 1, we can find the value of y:
10 + y = 14
y = 14 - 10
y = 4
So, Sharon has 10 one-dollar bills and 4 five-dollar bills.