eva is working two summer jobs, making $16 per hour tutoring and $8 per hour clearing tables. Last week eva worked 3 times as many hours clearing tables as she worked hours tutoring hours and earned a total of $80. Graphically solve a system of equations in order to determine

Answer

y = 3(2) = 6

Thus, she tutored for 2 hours and cleaned tables for 6 hours.

Explanation

These questions are all about writing down mathematically what they are saying in words. Use variables whenever there is an unknown, and try to write equalities based on what is said.

So, taking it one step at a time:

Eva is working two summer jobs,

Cool.

making $16 per hour and $8 per hour clearing tables.

I'm guessing this is $16/hr for tutoring, and $8/hr for clearing tables?

Last week Eva worked 3 times as many hours clearing tables as she worked tutoring hours

Let C = the number of hours Eva worked at clearing tables

Let T = the number of hours Eva worked at tutoring

Last week Eva worked C = 3 * T

and earned a total of $80.

The amount she earned at each place is:

8*C = money from clearing tables

16*T = money from tutoring

8*C + 16*T = 80

Solve a system of equations in order to determine the number of hours Eva worked tutoring last week, X, and the number of hours Eva worked clearing tables last week, Y,

Welp, I guess they wanted X and Y but it doesn't matter. From the equations above we can say:

8*C + 16*T = 80

C = 3*T

That should be enough to solve for:

C = ?

T = ?

Let x = # of hrs spent tutoring, y = # of hrs spent cleaning tables

We know she worked 3 times as many hours cleaning tables as she did tutoring, which implies:

3x = y

Also, her total earnings add up to $80, which implies:

16x + 8y = 80

This gives us the following system of equations:

3x = y

16x + 8y = 80

Let's make the substitution y = 3x into the 2nd equation:

16x + 8(3x) = 80

16x + 24x = 80

40x = 80

x = 2.

Next, plug in x = 2 into the first equation:

y = 3(2) = 6

Thus, she tutored for 2 hours and cleaned tables for 6 hours.