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.
Question
Answer:
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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11 months ago
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