Players on the school soccer team are selling candles to raise money for an upcoming trip. Each player has 24 candies to sell. If a player s

Question

Players on the school soccer team are selling candles to raise money for an upcoming trip. Each player has 24 candies to sell. If a player sells for candies, a profit of $30 is made. If he sells 12 candies, a profit of $70 is made. The profit And the number of candies sold form a linear relation. What is the slope and what does it mean in this problem?

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Ruby 7 days 2021-10-12T10:23:04+00:00 1 Answer 0

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    2021-10-12T10:24:18+00:00

    Answer:

    Slope, M  = 5  and this means that profit is five (5) times  every  unit change in the quantity of candies.

    Step-by-step explanation:

    Let the equation below represent the Profit and number of candies relationship:

    π (x) = Mx +c————————————————————— (1)

    Where  π = Profit

                x  = Number of candies sold

                M = Slope of the linear relationship/ equation

                 C = The profit intercept of the linear equation or relationship

    From the question two different coordinates of profit and the number of candies where given: (π₁ ,x₁)  and (π₂ ,x₂)

    First coordinate (π₁ ,x₁)  = ($30 , 4)

    Second coordinate (π₂ ,x₂)  = ($70, 12)

    These can be substituted into equation (1) and (2) to calculate the for M & C

    Substituting the first coordinate into (1) we have :

    30 =  4M +C—————————————————————–(2)

    Substituting the second coordinate into (1) we have :

    70 = 12M +C——————————————————————(3)

    Solving equation  (2) and (3) simultaneously using elimination method, we have:

    30 =  4M +C

    70 = 12M +C

    -40 = -8M

    M = 5

    Substituting the value of M into equation (3) we have:

    70 = 12(5) +C

    70 = 60 +C

    C =10

    Substituting the value of M and  C into equation (1), we have the Linear relationship for profit and the number of candies sold as

    π (x) = 5x + 10—————————————————————- (4)

    Slope  = 5  and this means that profit changes five (5) times for every  unit change in the quantity of candies.

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