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?

Answer 1

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

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.