Q:

# 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?

Accepted Solution

A:
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 relationshipFrom 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 & CSubstituting 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 +C70 = 12M +C-40 = -8MM = 5Substituting the value of M into equation (3) we have:70 = 12(5) +C70 = 60 +CC =10Substituting the value of M and  C into equation (1), we have the Linear relationship for profit and the number of candies sold asπ (x) = 5x + 10---------------------------------------------------------------- (4)Slope  = 5  and this means that profit changes five (5) times for every  unit change in the quantity of candies.