Cedric cashed a $125 check at the bank. The teller gave Cedric his money in $5 and $10 bills only. If the teller gave Cedric twice as many $10 bills as $5 bills, how many of each type did cedric receive?
number of fives --- x
number of tens ---- 2x
5x + 10(2x) = 125
25x = 125
x = 5
he was given 5 fives and 10 tens
To solve this problem, let's assume that Cedric received x number of $5 bills and y number of $10 bills.
According to the problem, Cedric cashed a $125 check at the bank. So, we know that the value of the $5 bills and $10 bills combined should equal $125. Therefore, we can set up the equation:
5x + 10y = 125
The problem also states that the teller gave Cedric twice as many $10 bills as $5 bills. This means that y (the number of $10 bills) is twice x (the number of $5 bills). Mathematically, we can represent this as:
y = 2x
Now, we have two equations:
5x + 10y = 125 (Equation 1)
y = 2x (Equation 2)
We can solve this system of equations to find the values of x and y.
From Equation 2, we can replace y in Equation 1 with 2x:
5x + 10(2x) = 125
5x + 20x = 125
25x = 125
x = 5
Substituting the value of x back into Equation 2:
y = 2 × 5
y = 10
Therefore, Cedric received 5 $5 bills and 10 $10 bills.