Question

A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 8000 shirts can be sold at a price of $27, while 13000 shirts can be sold at a price of $12. Give a linear equation in the form p=mn + b that gives the price p they can charge for n shirts. Answer: p = Round the value of your slope to three decimal places. Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer.

Answer 1

The linear equation where p s the price and n is the number of shirts sold is p = - 0.003n + 51.

A clothing company discovers a linear relationship between the maximum price it can charge per shirt, p, and the maximum number of shirts, n, it can sell.

In historical data,

The number of shirts sold is 8000 at a price of $27.

So, n = 8000 and p = $27

Using the linear equation in form p = mn + b

Then,

27 = 8000m + b                   -----------(1)

Now, 13000 shirts can be sold at a price of $12.

n = 13000, p = $12

Then,

12 = 13000m + b

b = 12 - 13000m                   -----------(2)

Substituting equation (2) in equation (1),

27 = 8000m + 12 - 13000m

- 5000m + 12 = 27

- 5000m = 27 - 12

- 5000m = 15

m = 15 / - 5000

m = - 3/1000 = - 0.003

Therefore,

27 = 8000m + b

b = 27 - 8000m

b = 27 - 8000 × ( - 0.003 )

b = 27 + 24 = 51

Then the linear equation is:

p = mn + b

p = - 0.003n + 51

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