A stack of $20, $50, and $100 was retrieved as part of a police investigation. There were 36 more $50 bills than $100 bills. Also, the number of $20 bills was 8 times the number of $100 bills. If the total value of the money was $9240, find the number of each type of bill.
A. The number of $100 bills was ____.
B. The number of $50 bills was ____.
C. The number of $10 bills was ____.
number of $100 bills ---- x
number of $50 bills ----- x+36
number of $20 bills ----- 8x
equations based on the value of the bills:
100x + 50(x+36) + 20(8x) = 9240
solve the equation and sub back into my definitions
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of $100 bills is x.
Since there were 36 more $50 bills than $100 bills, the number of $50 bills would be x + 36.
And since the number of $20 bills was 8 times the number of $100 bills, the number of $20 bills would be 8x.
Now, let's calculate the total value of the money in terms of the number of bills:
The value of x $100 bills is 100x.
The value of (x + 36) $50 bills is 50(x + 36).
The value of 8x $20 bills is 20(8x).
Based on the information given, the total value of the money is $9240. So, we can set up the equation:
100x + 50(x + 36) + 20(8x) = 9240
Now, let's solve this equation to find the value of x, which is the number of $100 bills:
100x + 50x + 1800 + 160x = 9240
310x + 1800 = 9240
310x = 7440
x = 24
Therefore, the number of $100 bills is 24.
To find the number of $50 bills, we substitute the value of x into the equation x + 36:
24 + 36 = 60
Therefore, the number of $50 bills is 60.
Finally, to find the number of $20 bills, we substitute the value of x into the equation 8x:
8 * 24 = 192
Therefore, the number of $20 bills is 192.
Hence,
A. The number of $100 bills is 24.
B. The number of $50 bills is 60.
C. The number of $20 bills is 192.