A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How

[math_celebrity]

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have?

Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations:

1. a + b = 44
2. 10a + 20b = 730

We rearrange equation 1 in terms of a. We subtract b from each side and we get:

1. a = 44 - b
2. 10a + 20b = 730

Now we substitute equation (1) for a into equation (2):
10(44 - b) + 20b = 730

Multiply through to remove the parentheses:
440 - 10b + 20b = 730

Group like terms:
440 + 10b = 730

Now, to solve for b, we type this equation into our search engine and we get:
b = 29

To get a, we take b = 29 and substitute it into equation (1) above:
a = 44 - 29
a = 15

So we have 15 ten-dollar bills and 29 twenty-dollar bills