How do I solve? Been working this problem for over an hour and I am more than stuck. I dont even know where to begin.

Question

Vince worked 18 hours last week. Part of the time he worked in a fast food restaurant and part of the time he worked tutoring high school kids in math. he was paid $7.25 per hour working in the restaurent and $15 per hour tutouring. He earned a total of 161.50         how many hours did he work each job?

Answer 1

Chris,

 

The thing about word problems is that they tell you everything you need to know.  You just need to try to write down what they tell you, but in mathematical form.

 

I'm going to assume that you are learning about how to solve systems of equations, such as two equations with two unknowns.  If not, then the same ideas apply but slightly differently, and Joshua's approach is totally correct.

 

So for example...

 

They want you to figure out how much time Vince worked in each job.  So start by assigning a variable name to each of the things they want you to figure out:

 

x = number of hours at the fast food restaurant

y = number of hours tutoring.

 

Now what else did they tell you?

 

1. He worked a total of 18 hours.  So that means that x + y = 18.  There's one equation already!

2. He makes $7.25/hour at the restaurant, and $15/hour tutoring.  So go back to the variables you set up.  You can tell you that he made 7.25 x at the restaurant and 15 y at tutoring.

3. He made a total of $161.50.  That means that you can add the amounts he made at each job to get to $161.50:  7.25 x + 15 y = 161.50.  There's your second equation.

 

Now you have two equations with two unknowns, and that means that you can solve the problem. 

 

A simple way is to use substitution, which would allow you to say that y = 18 - x.  You can plug this expression for y into the second equation, and it would leave you with one equation for x, which you can then go ahead and solve.

 

 

Answer 2

DEFINE VARIABLES

 

x=hours worked in fast food restaurant

18 - x=hours worked tutoring  (he worked a total of 18 hours so if i subtract from 18 the hours worked in fast food, I am left with hours worked tutoring)

 

SET UP EQUATIONS

 

I now multiply x by 7.25 to get the amount of money he made in the restaurant and I multiply (18-x) by 15 to get the amount of money he made tutoring. When I add these amounts together, I get 161.50 which is the total amount of money he made. 

 

7.25x + 15(18 - x) = 161.50 

 

SOLVE THE EQUATION

 

7.25x + 15(18 - x) = 161.50

7.25x + 270 - 15x=161.50

-7.75x=-108.5

x=14

 

Therefore, x=14. x was the number of hours he worked in the restaurant so he worked 14 hours in the restaurant.   18-x was the number of hours he spent tutoring so he spent 18-14=4 hours tutoring. 

 

ANSWER: He spent 14 hours in the restaurant and 4 hours tutoring