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?

For this case we have:

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

That is,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:

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

The minimum number of weeks is 6.

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

if x = 1, then the answer is 3.5