Algebra 1 Question

Question

Karen makes $5 per hour babysitting and $12 per hour giving music lessons. One weekend she worked a total of 18 hours and made $139. How many hours did she spend baby sitting?

Answer 1

Great question. We have to use a system of linear equations.

Let's make x the hours spent babysitting and y the hours giving music lessons by Karen.

We have to find x in this problem since it asks how many hours she spent babysitting.

Because we have two variables, x and y, we have to find two equations.

The first equation is simple.

x+ y = 18

Since she worked a total of 18 hours and x is the hours babysitting and y ins the hours giving music lessons.

The second equation is a little more tricky. We know that she made $139, which means that:

5x + 12y = 139 because she earned $5 per our babysitting and $12 per hour giving lessons.

5x is the total amount of money from babysitting and 12y is the total amount of money giving lessons, so adding them gives you $139.

We have our two equations:

5x + 12y = 139

x + y = 18

We have to solve for x, so we need to cancel out y. We can multiply our second equation by 12 and then subtract the two.

5x + 12y = 139

12x + 12y = 216 (-)

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-7x = -77

x = 11

She spent 11 hours babysitting.