Question

A sports team sells candles as a fundraiser. The revenue for selling x candles is given by f(x)=12x . The team's profit is $40 less than 80% of the revenue for selling x candles. Write a function g to model the profit. Then find the profit for selling 70 candles.

Answer 1

`g(x) = 9.6\cdot x -40`; The team shall earn $ 632 for selling 70 candles.

Explanation:

We notice that statement indicate that every worker gains 80 percent of the revenue for selling candles, which is represented
`f(x) = 12\cdot x`, where
`x` is the quantity of sold candles and
`f(x)` is measured in US dollars, minus 40 US dollars. Then, the mathematical expression
`g(x)` is formed by three components:

1) Revenue for selling candles:
`f(x)`

2) 80 % of the revenue for selling candles: Vertical scaling (
`k = 0.8`)

3) $ 40 are subtracted: Vertical translation. (
`b = -40`)

Then, the expression for
`g(x)` is:

`g(x) = k\cdot f(x) +b`

`g(x) = 0.8\cdot (12\cdot x) -40`

`g(x) = 9.6\cdot x -40`

Where:

`x` - Quantity of candles, dimensionless.

`g(x)` - Team's profit, measured in US dollars.

Finally, we determine the profit for selling 70 candles: (
`x = 70`)

`g(70) = 9.6\cdot (70) - 40`

`g(70) = 632`

The team shall earn $ 632 for selling 70 candles.