Question

You have $47 to spend at the music store. Each cassette tape costs $5 and each D costs $10. If `x` represents the number of tapes and `y` the number of CDs, what is the linear inequality that represents this situation?

Answer 1

Please see below.

Explanation:

As each cassette tape costs `$5` and each CD costs `$10`,

`x` number of tapes and `y` number of CDs will cost

`5xx x + 10 xx y=5x+10y`

i.e. one will have to pay `5x+10y` to purchase `x` number of tapes and `y` number of CDs.

But one cannot spend more than `$47` as that is the amount with me.

Hence we should have

`5x+10y<=47`

the linear inequality that represents this situation.

The solution will be given by
graph{5x+10y<=47 [-6.75, 13.25, -2.96, 7.04]}

and one can purchase `x` number of tapes and `y` number of CDs, where `x` and `y` are as per coordinates of a point in the shaded region.

But note that `x>=0` and `y>=0` as we cannot have negative number of tapes and negative number of CDs bur can choose no tapes or no CDs or both.

Hence, possible solutions are only integral values in `DeltaABC` below.