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A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
-When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84.
-When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A. (12, 20)
B. (15, 18)
C. (18, 15)
D. (20, 12)

Note: Please show work. My teacher checks it.

Respuesta :

EngrHanya
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)

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