Question

An automatic teller machine gives you $150 in five and ten-dollar bills.  There are two more than twice as many five-dollar bills as there are ten-dollar bills.  How many of each denomination are there?​

Answer 1

There are 7 ten-dollar bills and 16 five-dollar bills.

Explanation:

Let's call:

T: Number of ten-dollar bills

F: Number of five-dollar bills

The amount of money withdrawn from the ATM is $150:

10T+5F=150

Dividing by 5:

`2T+F=30\qquad\qquad [1]`

We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:

`F=2+2T\qquad\qquad [2]`

Substituting [2] into [1]:

2T+2T+2=30

Rearranging:

2T+2T=30-2

Simplifying:

4T=28

Solving:

T=28/4=7

From [2]:

F=2+2*7=2+14=16

There are 7 ten-dollar bills and 16 five-dollar bills.