MC

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- Rational Function
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- in Real Life
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- Presented by:
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- John Peter B. Carbonel
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- What is Rational Function?
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- - is any function that can be defined by a rational fraction.
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- - numerator and denominator are polynomials
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- f(x) = P(x)/Q(x)
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- P(x) and Q(x) are Polynomials, and Q(x) is not equal to 0
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- where,
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- Sample Problem
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- Elyn bought 85 kilograms of fruits consisting of Dalandan and Mango for her fruit stand business. She bought P1320 worth of dalandan and P3120 worth of Mango. If the cost per kilogram of mango is P20 more than that of dalandan, how many kilograms of each fruit did she buy?
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- Step 1
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- x = kilograms of Dalandan
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- 85-x = kilograms of Mango
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- Step 2
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- no. of kg bought
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- cost per kg
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- Total Cost
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- Mango
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- 1320
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- Dalandan
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- x
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- 1320/x
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- 3120
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- 85-x
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- 3120/80-x
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- Step 3
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- Cost per kg of mango = P20 + cost/kg of dalandan
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- 3120 85-x
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- = 20 +
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- 1320 x
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- 1320 x
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- = +
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- 20 1
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- 3120 85-x
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- 3120 85-x
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- =
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- 20x + 1320 x
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- Step 4
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- 20x + 1320 x
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- =
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- 3120 85-x
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- LCD
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- x (85 - x)
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- Step 5
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- (x) (85x)
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- ( )
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- 3120 85-x
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- =
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- ( )
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- 20x + 1320 x
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- (x) (85x)
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- 3120x = (20x + 1320)(85-x)
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- 3120x = (20x + 1320)(85-x)
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- 3120x = 1700x - 20x + 112,200 - 1320x
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- 2
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- 3120x = 20x +1700x - 1320x + 112,200
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- 2
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- 3120x = -20x + 380x + 112,200
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- 2
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- 20x + 3120x - 380x - 112,200 = 0
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- 2
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- 20x + 2740x - 112,200 20
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- 2
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- = 0
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- x + 137x - 5610 = 0
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- 2
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- Quadratic Formula
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- a=1 b=137 c=-5610
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- There are 33kg of Dalandan that Elyn bought.
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- Step 6
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- 3120 85-x
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- = 20 +
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- 1320 x
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- 3120 85-x
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- = 20 +
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- 1320 x
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- 60 = 60
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- x = 33 -> no. of Dalandan
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- 85 - x
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- 85 - 33 = 52
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- Elyn bought 85kg of Fruits