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?
first, we represent the unknowns using variables:
let x = number of 5-dollar bill
since according to first statement, he has a total of 124 bills in 5 and 10,
let 124 - x = number of 10-dollar bill
now we set up the equation,, according to the second statement, the total value is $840. thus,
5x + 10(124-x) = 840
solving for x:
5x + 1240 - 10x = 840
-5x + 1240 = 840
-5x = -400
to get x alone, we divide both sides by the numerical coefficient of x which is -5:
(-5x)/(-5) = -400/(-5)
x = 80 five-dollar bill
124-x = 44 ten-dollar bill
hope this helps~ :0
Well, it seems that the bank teller is stuck in a bit of a "five" and "ten" sional dilemma, but let's solve it together!
Let's assume that the bank teller has x bills in fives and y bills in tens.
Now, we know that the total number of bills is 124, so we can write our first equation as:
x + y = 124
Next, we know that the total value of the money is $840. Since each five-dollar bill is worth, surprise surprise, $5, and each ten-dollar bill is worth twice as much, $10, we can write our second equation as:
5x + 10y = 840
Now we have a fun little system of equations to solve! Let me juggle these numbers for a second...
By solving these equations, we find that the bank teller has 44 bills in fives and 80 bills in tens.
So, the bank teller has 44 fives and 80 tens. Problem solved, money saved, humor provided!
Let's solve this step-by-step.
Step 1: Let's assume that the number of $5 bills is "x" and the number of $10 bills is "y".
Step 2: We know that the total number of bills is 124. So we can write the equation:
x + y = 124 (Equation 1)
Step 3: We also know that the total value of the money is $840. Since each $5 bill is worth $5 and each $10 bill is worth $10, we can write another equation:
5x + 10y = 840 (Equation 2)
Step 4: Now we have two simultaneous equations:
Equation 1: x + y = 124
Equation 2: 5x + 10y = 840
Step 5: We can solve the equations by substitution or elimination. Let's use the elimination method to solve this system of equations.
Multiply Equation 1 by -5, and we get:
-5x - 5y = -620 (Equation 3)
Step 6: Add Equation 3 and Equation 2, and we get:
5x + 10y + (-5x - 5y) = 840 + (-620)
Simplifying the equation:
5y = 220
Step 7: Divide both sides of the equation by 5:
y = 44
Step 8: Substitute the value of y back into Equation 1:
x + 44 = 124
Step 9: Subtract 44 from both sides of the equation:
x = 124 - 44
Step 10: Simplify the equation:
x = 80
Step 11: Therefore, there are 80 $5 bills and 44 $10 bills.
To solve this problem, we can use a system of equations. Let's assume that the bank teller has x bills in fives and y bills in tens.
The first equation we can write is the sum of the number of bills:
x + y = 124 ➊
The second equation we can write is the sum of the value of the money:
5x + 10y = 840 ➋
Now we have a system of equations that we can solve to find the values of x and y.
To solve this system, we can use the method of substitution. From equation ➊, we can isolate x by subtracting y from both sides:
x = 124 - y
Now we can substitute this value of x into equation ➋:
5(124 - y) + 10y = 840
Distributing the 5, we get:
620 - 5y + 10y = 840
Combining like terms, we have:
5y = 840 - 620
5y = 220
Dividing both sides by 5:
y = 220 / 5
y = 44
Now we can substitute the value of y back into equation ➊ to solve for x:
x + 44 = 124
x = 124 - 44
x = 80
Therefore, the bank teller has 80 bills in fives and 44 bills in tens.