Question

Mark and John work the same amount of hours babysitting and tutoring. Mark gets paid $6 per hour for babysitting and $15 an hour tutoring. He makes $150 in one week. John makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114. How many hours were spent babysitting and tutoring?

a) 8 babysitting and 5 tutoring
b) 5 babysitting and 7 tutoring
c) 5 babysitting and 5 tutoring
d) 5 babysitting and 8 tutoring

Answer 1

Mark spent 4 hours babysitting and 28 hours tutoring. The correct answer is option d) 5 babysitting and 8 tutoring.

Step-by-step explanation:

Let's assume the number of hours spent babysitting by Mark and John is x, and the number of hours spent tutoring by Mark and John is y.

From the given information, we can form the following equations:

6x + 15y = 150 (equation 1)

10x + 8y = 114 (equation 2)

Multiplying equation 1 by -2 and adding it to equation 2, we get:

10x + 8y - 12x - 30y = 114 - 300

-2x - 22y = -186 (equation 3)

Now, multiplying equation 2 by 3 and adding it to equation 3, we get:

30x + 24y - 2x - 22y = 342 - 186

28x + 2y = 156 (equation 4)

Solving equations 3 and 4, we find:

28x + 2y = 156

-2x - 22y = -186

Multiplying equation 4 by 22 and adding it to equation 3, we get:

616x + 44y - 2x - 22y = 3432 + (-396)

614x + 22y = 3036 (equation 5)

Now, multiplying equation 4 by 614 and adding it to equation 5, we get:

17236x + 4400y + 614x + 22y = 9408 + 3036

17850x + 4422y = 12444 (equation 6)

Multiplying equation 6 by 4 and equation 5 by 4422, we get:

71400x + 17688y = 49776

71400x + 19320y = 94676

Subtracting the equations, we have:

1603y = 44900

y = 28

Substituting the value of y in equation 5, we get:

614x + 22(28) = 3036

614x + 616 = 3036

614x = 2420

x = 4

Therefore, Mark spent 4 hours babysitting and 28 hours tutoring.

So, the correct answer is option d) 5 babysitting and 8 tutoring.