Cole needs at least $815 to cover travel and hotel expenses for an upcoming national singing competition. He is setting up a weekly singing gig at a local coffee shop to pay for the costs. If the coffee shop agrees to pay him $125 each week after he made $65 at an open mic night at the shop, how many weeks could Cole perform to raise the amount he needs for the competition?

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DrunKMediC DrunKMediC · Answer 1 · 2018-10-22T07:48:04+02:00

It would take 6 weeks for Cole to make 750$ and the 65$ he had received from the open mic would make it 815$

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carlosego carlosego · Answer 2 · 2018-10-22T16:15:31+02:00

For this case we have:

Let x be the number of weeks you should work in the store. We have:

[tex]125x + 65 \geq 815[/tex]

That is,[tex]125x[/tex]represents the profit obtained according to the number of weeks worked.

65, represents the gain obtained in one night, in the store.

Cole's earnings must be greater than or equal to the cost of the trip and stay of the singing competition, so he can cover it.

Clearing x:

[tex]125x\geq 815-65\\ 125x\geq 750[/tex]

[tex]x \geq\frac{750}{125}[/tex]

[tex]x \geq6[/tex]

Thus, the minimum number of weeks that Cole must work to cover the costs of the competition is 6.

Answer:

The minimum number of weeks is 6.

[tex]x \geq6[/tex]