A cashier has a total of 126 bills, made up of fives and tens. The total value of money is $890. How many ten-dollar bills does the cashier have?
5F+10T=890
F+T=126
multiply the second equation by 5, then subtract the equation from the first.
5F+10T=890
5F+5T=630
then subtract equations
5T=360
T=72
check all that.
Let the fives and tens be represented by 5x +10y=890, x +y =126 solve by elimination . X =74.. y =52
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the cashier has x ten-dollar bills and y five-dollar bills.
According to the problem, the cashier has a total of 126 bills:
x + y = 126 -- Equation 1
The total value of the money is $890:
10x + 5y = 890 -- Equation 2
Now we have a system of equations. To solve it, we can use the method of substitution or elimination.
Method 1: Substitution
Solve Equation 1 for y:
y = 126 - x
Substitute the value of y in Equation 2:
10x + 5(126 - x) = 890
Now, simplify and solve for x:
10x + 630 - 5x = 890
5x = 260
x = 52
Substitute the value of x in Equation 1 to find y:
52 + y = 126
y = 74
Therefore, the cashier has 52 ten-dollar bills and 74 five-dollar bills.
Method 2: Elimination
Multiply Equation 1 by 5 to make the coefficients of y in both equations the same:
5(x + y) = 5(126)
5x + 5y = 630 -- Equation 3
Subtract Equation 3 from Equation 2:
(10x + 5y) - (5x + 5y) = 890 - 630
5x = 260
x = 52
Substitute the value of x in Equation 1 to find y:
52 + y = 126
y = 74
Again, we find that the cashier has 52 ten-dollar bills and 74 five-dollar bills.
So, the cashier has 52 ten-dollar bills.