Question

An entertainment firm offers several DJ choices and light shows that range in price based on the rental time period. The DJ's cost between $219.00 and $369.00 per night and the light shows cost between $159.00 and $309.00 per night. If you are booking both a DJ and a light show, write a compound inequality that represents the possible total amount you would pay, x.

Answer 1

`378<x<678`

Explanation:

Given : The DJ's cost between $219.00 and $369.00 per night and the light shows cost between $159.00 and $309.00 per night.

To Find: If you are booking both a DJ and a light show, write a compound inequality that represents the possible total amount you would pay, x.

Solution:

Let x be the total amount for both a DJ and a light show

DJ's cost between $219.00 and $369.00 per night

The light shows cost between $159.00 and $309.00 per night.

Minimum cost for Dj and light show both =Minimum DJ cost +Minimum light show cost

= 219+159

= 378

Maximum cost for Dj and light show both =Maximum DJ cost +Maximum light show cost

= 369+309

= 678

So, Compound inequality:Minimum cost for Dj and light show both <x<Maximum cost for Dj and light show both

Compound inequality:
`378<x<678`

Hence a compound inequality that represents the possible total amount you would pay, x. is
`378<x<678`