a 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?
Let x = $5 bills and y = $10 bills
x + y = 124
x = 124-y
5x + 10y = 840
Substitute 124-y for x in third equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the last equation.
Let's solve this problem step-by-step:
Step 1: Determine the variables
Let x be the number of five-dollar bills and y be the number of ten-dollar bills.
Step 2: Set up the equations
We can create two equations based on the given information:
Equation 1: x + y = 124 (since there are 124 bills in total)
Equation 2: 5x + 10y = 840 (since the total value of the money is $840)
Step 3: Solve the equations
To solve the system of equations, we can use the substitution method or the elimination method. In this case, let's use the elimination method.
Multiply Equation 1 by 5 to make the coefficients of x in both equations the same:
5(x + y) = 5(124) becomes 5x + 5y = 620
Subtract Equation 2 from this new equation:
(5x + 5y) - (5x + 10y) = 620 - 840
5x + 5y - 5x - 10y = -220
-5y = -220
Divide both sides of the equation by -5:
-5y / -5 = -220 / -5
y = 44
Now substitute y = 44 into Equation 1:
x + 44 = 124
x = 124 - 44
x = 80
Step 4: Find the solution
Based on the calculations:
The bank teller has 80 five-dollar bills and 44 ten-dollar bills.
Therefore, the bank teller has 80 five-dollar bills and 44 ten-dollar bills.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of five-dollar bills is represented by 'x', and the number of ten-dollar bills is represented by 'y'.
From the problem statement, we have two pieces of information:
1) The total number of bills: x + y = 124
2) The total value of the money: 5x + 10y = 840
We can solve this system of equations to find the values of 'x' and 'y'.
To eliminate one variable, let's multiply the first equation by 5:
5(x + y) = 5(124)
5x + 5y = 620
Now, let's subtract this new equation from the second equation to eliminate 'x':
(5x + 10y) - (5x + 5y) = 840 - 620
5y = 220
Dividing both sides by 5, we find:
y = 44
Now, substitute this value of 'y' back into the first equation to solve for 'x':
x + 44 = 124
x = 124 - 44
x = 80
Therefore, the bank teller has 80 five-dollar bills and 44 ten-dollar bills.