Question

A cattle rancher is going to sell one of his prize bulls at an auction and would like to make $36,400 after paying a 9% commission to the auctioneer. For what selling price will the rancher make this amount of money?

Answer 1

$40,000

Explanation:

Let x represent the selling price of the bull.

We have been given that a cattle rancher would like to make $36,400 after paying a 9% commission to the auctioneer.

The commission would be 9% of selling price, that is
`(9)/(100)x=0.09x`.

The profit of the rancher can be counted after paying off the commission that would be
`x-0.09x`.

Since rancher wants to make $36,400 after paying a 9% commission, so we can represent this information in an equation as:

`x-0.09x=36,400`

`0.91x=36,400`

`(0.91x)/(0.91)=(36,400)/(0.91)`

`x=40,000`

Therefore, for a selling price of $40,000 the rancher will make the required amount of money.