After paying mom, you find that you have 13 bills. The number of ten dollar bills you have is twice the number of five dollar bills. The number of one dollar bills is two less than six times as many ten dollar bills. Find the number of each bill that you have. Write an equation to solve it.
t + f + o = 13
t = 2 f
o + 2 = 6 t
=========================
2 f + f + (6t-2) = 13
3 f + (12f-2) = 13
15 f = 15 remarkable, whole number :)
t = 2 f
o = 6t-f
To solve this problem, let's assign variables to represent the number of each type of bill.
Let:
- "x" be the number of five dollar bills,
- "2x" be the number of ten dollar bills,
- "6(2x) - 2" be the number of one dollar bills.
Now, let's set up an equation based on the given information and solve for the values.
According to the problem, the total number of bills is 13. Therefore, we can write the equation:
x + 2x + 6(2x) - 2 = 13
Simplifying the equation:
x + 2x + 12x - 2 = 13
15x - 2 = 13
Adding 2 to both sides of the equation:
15x = 15
Dividing both sides of the equation by 15:
x = 1
Now, we can substitute the value of x back into the variables to find the number of each bill:
The number of five dollar bills (x) = 1
The number of ten dollar bills (2x) = 2
The number of one dollar bills (6(2x) - 2) = 6(2) - 2 = 10
Therefore, you have 1 five dollar bill, 2 ten dollar bills, and 10 one dollar bills.