Amanda has $227 worth of bills in her purse. She has 6 more $5 bills than $10 bills. The number of $1 bills is three fewer than 25 times the number of $10 bills. How many bills of each kind does Amanda have?
# of tens: 5
# of fives: 11
# of ones: 122
thanks oobleck
To solve this problem, we can set up a system of equations to represent the given information. Let's assign variables to the unknowns:
Let's say the number of $10 bills Amanda has is 'x'.
Therefore, the number of $5 bills she has will be 'x + 6' (as she has 6 more $5 bills than $10 bills).
The number of $1 bills will be '25x - 3' since it is three fewer than 25 times the number of $10 bills.
Now let's use the information about the total value of bills to create an equation:
10x + 5(x + 6) + 1(25x - 3) = 227
Let's solve this equation step by step:
First, distribute the 5 and 1 terms:
10x + 5x + 30 + 25x - 3 = 227
Combine like terms:
40x + 27 = 227
Next, isolate the x term by subtracting 27 from both sides:
40x = 200
Now, divide both sides by 40 to solve for x:
x = 5
So, Amanda has 5 $10 bills.
To find the number of $5 bills, substitute this value of x back into 'x + 6':
5 + 6 = 11
Amanda has 11 $5 bills.
To find the number of $1 bills, substitute the value of x into '25x - 3':
25(5) - 3 = 122
Amanda has 122 $1 bills.
Therefore, Amanda has 5 $10 bills, 11 $5 bills, and 122 $1 bills.
Count the bills, and count the values.
# of tens: x
# of fives: x+6
# of ones: 25x-3
so,
10x + 5(x+6) + 1(25x-3) = 227
now do your magic.