Question

Question #5bf27

Answer 1

1) $(225+80n), where n refers to the number of hours Jenna's band used.
2)`225+80n<555`, or `n<33/8`

Explanation:

1) As Jenna's band is using the recording studio for one day, they have to pay $225 for the room. However, as the number of hours they will be using is unknown, let's denote the number of hours be n.
For each hour, they have to pay an extra of $80 for sound technicians. Hence, for n-hour used, they will have to pay $80n.
Adding up the two costs, that gives the answer `$(225+80n)`.

2) It is given that the amount of money to be used (or the cost) is between `$205` and `$(205+350)`, which is `$555`.

Hence, we can derive an equation like this:
`205<225+80n<555`

As n must be a positive integer, 225+80n must be larger than 225, and hence must be larger than 205. The equation can then be simplified as

`225+80n<555`

`80n<555-225`

`80n<330`

`n<330/80`

`n<33/8`

Note: as `33/8=4.125`, assuming that Jenna's band uses an INTEGRAL number of hours, the equation becomes `n<5`, i.e.`n=1,2,3 or 4`.