A cash drawer has $267.00 total. There are no bills larger than a 10. There are 11 tens and 7 more 1s than 5s. How many of each bill is there?
To find the number of $5 bills, add up the value of all the bills and solve for f:
10*11 + 5*f + 1*(f+7) = 267
110.00 + 125.00 + 32.00 =267.00
To solve this problem, let's break it down into smaller steps.
Step 1: Let's assume the number of $5 bills is "x". So, the number of $1 bills would be "x + 7". We can now express the total value of the $5 and $1 bills in terms of "x".
Value of $5 bills = $5 * (number of $5 bills) = 5x
Value of $1 bills = $1 * (number of $1 bills) = 1 * (x + 7) = x + 7
Step 2: We know that the total value of the cash drawer is $267. So, we can write the equation:
Total value of the cash drawer = Value of $10 bills + Value of $5 bills + Value of $1 bills
$267 = $10 * (number of $10 bills) + 5x + (x + 7)
Step 3: We know that the number of $10 bills is 11. So, we can substitute it into the equation:
$267 = $10 * 11 + 5x + (x + 7)
Step 4: Simplify the equation:
$267 = $110 + 5x + x + 7
$267 = $117 + 6x
Step 5: Bring all the variables to one side and all the constants to the other side:
$267 - $117 = 6x
$150 = 6x
Step 6: Divide both sides of the equation by 6 to solve for "x":
$150 / 6 = x
x = 25
Now we know that there are 25 $5 bills.
Step 7: Calculate the number of $1 bills:
number of $1 bills = x + 7 = 25 + 7 = 32
So, there are 25 $5 bills and 32 $1 bills in the cash drawer.