Charles opened the old trunk and found $6750 in $1 bills and $10 bills. If there were 150 more ones than tens, how many of each kind were there?
Let x = the number of tens
10x= the value of the tens
x+150 = the number of ones and the value
10x+x+150=6750
11x=6600
x=600 10's and 750 1's
To find the number of $1 bills and $10 bills in Charles' trunk, we can set up a system of equations based on the given information.
Let's assume the number of $10 bills is x. Since there were 150 more $1 bills than $10 bills, the number of $1 bills would be x + 150.
Now, let's calculate the total value of the bills. The value of the $1 bills would be $1 times the number of $1 bills (x + 150). Similarly, the value of the $10 bills would be $10 times the number of $10 bills (x).
Given that the total amount in the trunk was $6750, we can set up the equation:
($1 bills value) + ($10 bills value) = $6750
($1)(x + 150) + ($10)(x) = $6750
Simplifying the equation, we have:
x + 150 + 10x = 6750
Combining like terms, we get:
11x + 150 = 6750
Now, let's isolate x by subtracting 150 from both sides:
11x = 6600
Dividing both sides by 11, we find:
x = 600
So, there were 600 $10 bills.
To find the number of $1 bills, we'll substitute this value of x back into our expression for the number of $1 bills:
x + 150 = 600 + 150 = 750
Thus, there were 750 $1 bills.
Therefore, Charles found 600 $10 bills and 750 $1 bills in the old trunk.