McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Geometric Probability
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Exercise 41 Page 905

Divide the area of the room by the area covered by one gallon of paint.

F

Practice makes perfect
We know that the area of Miki's room is x^2+8x+12 square feet, and a gallon of paint is enough to cover an area of x^2+6x+8 square feet. We want to choose the expression that gives the number of gallons of paint Miki will need to buy to paint her room. To do so, we will divide the area of Miki's room by the area covered by one gallon of paint. Number of Gallons &= Area of the Room/Area Covered by a Gallon &⇕ Number of Gallons &= x^2+8x+12/x^2+6x+8 To simplify this expression, we will factor each of the quadratic expressions as much as possible and then cancel any common factors.
Number of Gallons = x^2+8x+12/x^2+6x+8
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Factor
Number of Gallons = x^2+6x+2x+12/x^2+4x+2x+8
Number of Gallons = x(x+6)+2x+12/x(x+4)+2x+8
Number of Gallons = x(x+6)+2(x+6)/x(x+4)+2(x+4)
Number of Gallons = (x+2)(x+6)/x(x+4)+2(x+4)
Number of Gallons = (x+2)(x+6)/(x+2)(x+4)
Number of Gallons = (x+2)(x+6)/(x+2)(x+4)
Number of Gallons = x+6/x+4
The number of gallons of paint Miki needs to buy is x+6x+4, which corresponds to answer F.