2. Tú creas una empresa de venta de camisetas estampadas. Encuentras que por un precio de $5.00 por cada camisa logras vender 1800 camisetas al mes. Si el precio de cada camiseta es de $7.00, solo logras vender 1450 camisetas. A. Presumiendo que el número de camisetas vendidas se puede modelar de forma lineal en función del precio de cada camiseta, determina la ecuación que modela el número total de camisetas vendidas en un mes. (5 ptos.) b. ?Qué significa la pendiente? (2 ptos.) c. Tú dejas a un empleado en la venta de las camisas. Este pone un precio y solo logró vender 1525 camisas. ?Cuál fue el precio de las camisas?

You set up a company selling stamped t-shirts. You find that for a price of $5.00 per shirt you can sell 1800 t-shirts per month. If the price of each t-shirt is $7.00, you can only sell 1450 t-shirts. A. Assuming that the number of shirts sold can be modeled linearly based on the price of each shirt, determine the equation that models the total number of shirts sold in a month. (5 pts.) b. What does slope mean? (2 pts.) c. You leave an employee in the sale of shirts. This one puts a price and only managed to sell 1525 shirts. What was the price of the shirts?

Let

x-------> the price of the t-shirts

y------> the number of t-shirts sell per month

[tex]A(5,1,800),B(7,1,450)[/tex]

Part A) Find the equation of the linear equation

calculate the slope

[tex]m=(1,450-1,800)/(7-5)=-175\frac{\ shirts\ sell}{\$}[/tex]

Find the equation

with m and the point A

[tex]y=mx+b[/tex]

substitute and solve for b

[tex]1,800=-175(5)+b[/tex]

[tex]b=1,800+875=2,675[/tex]

the equation of the line is

[tex]y=-175x+2,675[/tex]

Part B) What does slope mean?

The slope is equal to

[tex]m=-175\frac{\ shirts\ sell}{\$}[/tex]

so

For every dollar that the price increases, the sale of shirts decreases by 175 units

Part C) You leave an employee in the sale of shirts. This one puts a price and only managed to sell 1525 shirts. What was the price of the shirts?

For [tex]y=1,525\ shirts[/tex]

substitute the value of y in the equation and solve for x

[tex]1,525=-175x+2,675[/tex]

[tex]175x=2,675-1,525[/tex]

[tex]x=1,150/175=\$6.57[/tex]