$5 per hour for baby sitting and $12 giving music lessons. In a week there was a total of 18 hours and she made $139. How many hours did she spend babysitting?

Question

I struggle with word problems like this so if anyone could help it would be greeeaatt thanks and it ight look weird because i had to shorten the question 

Answer 1

Hi Abby,

 

One hour of babysitting equals five dollars. This is represented by 5x.

One hour of music lessons equals 12 dollars. This is represented by 12y.

You have to use different variables (x and y) since babysitting and music lessons are two different things. 

 

Your first equation is your cost equation: 5x (babysitting) + 12y (music lessons) = $139.

 

Your second equation is the quantity equation: x (babysitting) + y (music lesson) = 18 (total number of hours)

 

5x + 12y = 130

  x +    y  = 18

 

When you have a system of equations (2 equations is called a system), you get to multiply one equation by a number that will let you cancel out a variable (either x or y).

 

In this case, let's cancel out 5x. It's a smaller number, and 5 is easier to multiply than 12.

 

Your first equation will not change. In your second equation, you will multiply each term by -5.

 

5x + 12y = 139.

-5x - 5y  = - 90

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Now you will combine the terms as they are lined up. Notice that 5x and -5x cancel out. 

 

5x + 12y = 139

-5x - 5y  = - 90

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0   + 7y   =  49

        

Divide both sides by 7.

 

7y = 49

y = 7.

 

Remember that y is the number of hours spent on music lessons. When you plug 7 into x + y = 18, you will find that x, the number of hours babysitting, equals 11.