Question

A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.

Answer 1

The answer is B. (15,18)

Solution:

First, let's set the variables first.

X = dollars per hour to clean the floor
Y = dollars per hour to clean the rest of the house

For the first statement, "2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84"
We can put it into an equation.
         2X + 3Y = 84       ⇒    equation 1

For the first statement, "1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87'
         X + 4Y = 87         ⇒    equation 2

Multiply first equation 2 by 2 to make the coefficient of both equations 1 and 2 the same.

Using elimination method in solving for x and y,

   (equation 1)              2X + 3Y = 84
   (equation 2)            2(X + 4Y) = 87   
                                    2X + 8Y = 174  ⇒ equation 3

Next, subtract equation 3 from equation 1.
            2X + 3Y = 84
      -   (2X + 8Y = 174)
        -------------------------
                  - 5Y = -90
                      Y = 18

Find X when Y = 18
@ equation 1  :    2X + 3Y = 84
                            2X + 3(18) = 84
                            2X + 54 = 84
                            2X = 84 - 54
                            2X = 30
                             X = 15
   
The answer is in ordered pairs of cleaning the floors and to clean the rest of the house. So, in the form (X,Y).

Answer: (15,18)