Algebra Word Problem

Question

Claire is working two summer jobs, making $7 per hour washing cars and making $15 per hour clearing tables. In a given week, she can work at most 9 total hours and must earn a minimum of $90. If x represents the number of hours washing cars and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution. Find two y inequalities.

Answer 1

Hey, so let us start solving this by writing down what is given to us.

We know that Claire can work a maximum of 9 hours, and she is doing two jobs.

so, let us say that x represents washing cars job, and y represents clearing tables job.

Now, we can write the equation x+y = 9, assuming that she did work for 9 hours.

Then, we were given that she gets paid $7 for her car washing job and $15 for clearing tables.

So, that means if she is working for two hours, she is getting paid $14 for a car washing job and $30 for clearing tables.

Given that, let us assume she works "x" hours at car washing job and "y" hours at clearing tables job.

So, that would give us the equation : 7x+ 15y =90 ( equals 90 because she wants to ear a minimum of 90)

Now, we have two equations:

x+y =9

7x+15y=90

From here, you can solve for x or y in the first equation, and then substitute that into the second equation.

So, I will solve for x in the first equation

x= 9-y

Now, you have to submit x= 9-y into the second equation to solve for y

7(9-y) +15y = 90

63-7y+15y = 90

8y+63 =90

8y= 27

y= 3.37

Now that we know our "y" value, we can easily solve for x

x= 9-3.37

x= 5.63

Hope this helps!