Question

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Answer 1

The equation that models the price - sales relationship is

y = - 500x + c and the total amount of sale will be 1250.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the scenerio describing the price - sales relationship for a toy.

Assume that the linear equation is of the form -

y = mx + c

Now, suppose [x] denotes the price and [y] denotes the amount of sale.

Now at -

[x] = 6, [y] = 2000

[8] = 8, [y] = 2000 - 1000 = 1000

The coordinates through which the line passes, will be -

(6, 2000) and (8, 1000)

We know that [m] denotes the slope of the line and it can be calculated as -

m = {y(2) - y(1)} / {x(2) - x(1)}

m = (1000 - 2000)/(8 - 6)

m = - 1000/2

m = - 500

Now, the equation becomes -

y = -500x + c

Substituting point (6, 2000) in it, we get -

2000 = - 500 x 6 + c

2000 + 3000 = c

c = 5000

So, the final equation will become -

y = - 500x + 5000

If x = $7.5, the total sales would be -

y = - 500 x 7.5 + 5000 = 1250

Therefore, the equation that models the price - sales relationship is

y = - 500x + c and the total amount of sale will be 1250.

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