Question

You sell your bicycle to your friend for 65$ your friend gives you x five dollar bills and y ten dollar bills. There are a total of 9 bills. How many five dollar and ten dollars bills did your friend give you?

Answer 1

There are
`5` five dollar bills and
`4` ten dollar bills.

Explanation:

Given:

Selling price of bicycle
`=\$65`.

The friend gave
`x` five dollar bills and
`y` ten dollar bills.

Total number of bills
`=9`.

To find: Number of five dollar bills and ten dollar bills the friend gave.

Solution:

The friend gave
`x` five dollar bills and
`y` ten dollar bills and the friend gave
`9`bills in all.

So,
`x+y=9`.

`\Rightarrow x=9-y ...(i)`

Selling price of bicycle
`=\$65`.

So,
`5x+10y=65...(ii)`

Putting the value of
`x` from equation
`(i)` in equation
`(ii)`.

`\Rightarrow 5(9-y)+10y=65`

`\Rightarrow 45-5y+10y=65`

`\Rightarrow 45+5y=65`

`\Rightarrow 5y=65-45`

`\Rightarrow 5y=20`

`\Rightarrow y=(20)/(5)`

`\Rightarrow y=4`

Now, putting the value of
`y` in equation
`(i)`.

`\Rightarrow x=9-4`

`\Rightarrow x=5`

Hence, there are
`5` five dollar bills and
`4` ten dollar bills.