Jared, the bank teller, has a total of 124 bills in fives and tens. The total value of the money is $840. How many of each kind does he have?
5F+10T=840
F+T=124
F=124-T
5(124-T)+10T=840
solve for T first, then solve for the fives.
23
To solve this problem, we can set up a system of equations. Let's assume that Jared has x five-dollar bills and y ten-dollar bills.
Based on the given information, we know two things:
1. The total number of bills is 124: x + y = 124
2. The total value of the money is $840. The value of each five-dollar bill is 5, and the value of each ten-dollar bill is 10: 5x + 10y = 840
We can use these two equations to solve for the unknown variables x and y.
First, let's solve the first equation for x:
x + y = 124
x = 124 - y
Now substitute this value for x in the second equation:
5(124 - y) + 10y = 840
Simplify the equation:
620 - 5y + 10y = 840
5y = 840 - 620
5y = 220
y = 220/5
y = 44
Now that we know the value of y is 44, we can substitute it back into the first equation to find x:
x + y = 124
x + 44 = 124
x = 124 - 44
x = 80
Therefore, Jared has 80 five-dollar bills and 44 ten-dollar bills.