(1) Jan owns a coffee shop. She is planning to hire Michael as a part time worker at $8.50 per hour.  She will also contribute $20 each week to a bonus fund, to be paid out at a later date. ...

(1) Jan owns a coffee shop. She is planning to hire Michael as a part time worker at $8.50 per hour.  She will also contribute $20 each week to a bonus fund, to be paid out at a later date.  Michael cannot work more than 35 hours a week.  How much will it cost Jan to hire Michael during his first to  2- week pay period?

(2) Ravi is planning to buy concert tickets for himself and a small group of his friends. The tickets cost $21each plus a transaction fee of $5. He is not sure how many of  his friends are going to the concert. How much can Ravi expect to spend for tickets?

Write the equation for the problem. Then use your equation to answer the question.  Show all work and explain your reasoning

Asked on by taylorruth

3 Answers | Add Yours

lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

(1) To solve, let x be the number of hours that Micheal work for each week. And let y be the number of weeks that he worked. And, let's assume that he worked same number of hours for each week.

If he worked for x hours for each week and for y weeks, to compute for his basic salary, multiply his hourly rate by the number of hours and weeks.

Basic Salary `= 8.5 * x * y =8.5xy`

Also, consider the bonus fund that he received for each week. To get his total bonus fund, multply $20 by the number of weeks that we worked.

Bonus Fund Paid `= 20*y = 20y`

So, his total salary is:

Total Salary `= 8.5xy + 20y`

Next, let's consider the given number of weeks. To solve for his total salary for the first two weeks, plug-in y=2 to the equation above.

Total Salary `= 8.5x(2) + 20(2) = 17x + 40`

So his total salary for the first two weeks can be computed using the equation:

Total Salary `= 17x + 40`

Since Micheal can not work more than 35 hours a week, his maximum number of hours for each week is 35 hours. So to compute for his maximum salary for the first two weeks plug-in x=35.

Total Salary `= 17x + 40`

Total Salary_(Max) `= 17(35)+40`

Total Salary_(Max) `=635`

So, Micheal's maximum salary for the firt two weeks is $635.

Therefore, it will cost Jan a maximum of $635 to hire Micheal for the first two-week pay period.

(2) To solve, let x be the number of Ravi's friends that are going to the concert. Then, determine the cost of the ticket that Ravis will have for himself and for his friends.

For himself, the cost of the ticket is $21.

For his friends, to get the cost of the tickets bought, multiply the unit price and the his number of friends going to the concert.

21*x

So, the cost of the ticket that he bought for his friends is 21x dollars.

Then, solve for the total cost of the tickets that he bought for himself and for his friends. Since there is additional transcation fee of $5, to get the total cost add $21, 21x dollars and $5.

Cost of all the tickets bought `= 21 + 21x + 5 = 21x + 26`

Since the number of Ravi's friends going to the concert is not given, there is no specific amount that Ravi can spend for tickets. We would only have the equation to compute for it.

Therefore, the cost of the tickets Ravi bought can be computed using the equation

`C=21x + 26` .

udonbutterfly's profile pic

udonbutterfly | Student, College Freshman | (Level 1) Valedictorian

Posted on

1) Michael is only able to work 35 hours a week so you are going to multiple that to the $8.50 that Jan is going to be paying him per hour. Also you are going to add the $20 bonus she pays every week for the position so you will get

8.50(35) + 20= c . C being the total cost of that week. To make it into a 2-week pay period you will multiply the entire equation by 2 so  2 x (8.50(35) + 20)

this equation will give you the answer $635 for the span of two weeks

2) This answer is a little unclear since there is no guaranteed way to know how much Ravi is going to spend on tickets since we do not know how many friends he's considering taking. However if here were to buy all the tickets at once and only do one transaction the equation would look like 21x +15= the amount he will need to spend. x being the amount of tickets he plans on purchasing.

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

1.) If Jan pays Michael $8.50 an hour for 35 hours a week, plus a $20 weekly bonus, and she pays him for two weeks, the equation you'd use is

2(8.50x+20)

2(8.50(35)+20)

2(297.50+20)

2(317.50)

=$635

2.) If Ravi spends $21 per ticket, plus a one time $5 transaction fee, the equation you'd use is

21x+5

There is no way to tell how much money he'll spend without knowing how many tickets he is required to by.

We’ve answered 318,979 questions. We can answer yours, too.

Ask a question