Question

Priya’s mom is trying to decide between two plumbers to fix her sink. The first plumber
charges ₹ 50 for his service call , plus an additional charge ₹36 per hour for labour. The
second plumber charges ₹ 35 for his service call , plus an additional charge ₹39 per hour for
labour. At how many hours will the two plumbers charge the same amount of money?
Represent the situation graphically.

Answer 1

Answer:

ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and