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Answer:
15 $1 bills
10 $5 bills
10 $10 bills
Step-by-step explanation:
Let x = number of $1 bills
"There are five fewer $5-bills than $1-bills."
The number of $5 bills is x - 5
"There are half as many $10-bills as $5-bills."
The number of $10 bills is (x - 5)/2.
A $1 bill is worth $1.
x $1 bills are worth x × 1 = x dollars
A $5 bill is worth $5.
x - 5 $5 are worth 5(x - 5) dollars.
A $10 bill is worth $10.
(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.
Now we add the value of each type of bills and set it equal to $115.
x + 5(x - 5) + 5(x - 5) = 115
x + 10(x - 5) = 115
x + 10x - 50 = 115
11x = 165
x = 15
There are 15 $1 bills.
$5 bills: x - 5 = 10 - 5 = 10
There are 10 $5 bills
$10 bills: (x - 5)/2 = (15 - 5)/2 = 5
There are 5 $10 bills
Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills
Check:
First, we check the total value of the bills.
15 $1 bills are worth $15
10 $5 bills are worth $50
10 $10 bills are worth $50
$15 + $50 + $50 = $115
The total does add up to $115.
Now we check the numbers of bills of each denomination.
The number of $1 is 15.
The number of $5 is 5 fewer that 15, so it is 10.
The number of $10 bills is half the number of $5 bills, so it is 5.
All the given information checks out in the answer. The answer is correct.