Need someone to tell me what I did wrong and how to correct it

[Akira9184]

I don't understand this assignment 100%. Please, someone help me so that I can finally stop stressing about it.

When the fundraiser began, 600 people wanted to purchase the dance troupe’s T-shirts at $12 per T-shirt, but as the group increased the price of their T-shirts, they noticed a fall in the demand. For every $1 increase in price, the demand fell by 50 shirts. The dance troupe’s initial supply was short by 210 T-shirts which corresponded to an initial price of $9.75. For every $1 increase in price, they ordered 40 more T-shirts. Write a system of linear equations to represent both the demand and supply for the T-shirts. Let q represent the quantity of T-shirts and p represent the price.

p = mq + b

Demand:
q = -50p + 1200

Supply:
q = 40p -180




Use the system of linear equations you wrote to solve for the variables p and q. Show all work.

Line 1:
(y2 – y1) – (x2 – x1)
= (12 – 11) – (90 – 50)
= 1/40

p = mq + b:
p = 1/40q + b
11 = 1/40 (90) + b
11 = ¼ (9) + b
11 = 9/4 + b
11 (4) = 9 + b
44 = 9 + b
44 – 9 = b
35 = b

p = 1/40q + 35


Line 2:
(y2 – y1) – (x2 – x1)
= (10 – 11) – (100 – 50)
= -1/50

p = -1/50q + b
10 = -1/50 (100) + b
10 = -1 (2) + b
10 = -2 + b
10 + 2 = b
12 = b

p = -1/50 + 12



The values for p and q represent the equilibrium point. As related to the troupe’s fundraiser, what does the equilibrium point represent?

The equilibrium point represents the two lines meeting, meaning when they have the same demands.
What happens when the quantity is above the equilibrium point?
When the quantity is above point that means the price is higher as well as the shirts. People won’t get enough shirts so they won’t be able to buy.
What happens when the quantity is below the equilibrium point?
When the quantity is below the point people will be able to buy as many shirts because the price is low.

 

[Dr.Peterson]

I'm confused, too.

You seem to have determined (correct) demand and supply equations, which you could have solved for p, but instead you (incorrectly) made new equations. One error is where you multiplied 11 = 9/4 + b by 4, but forgot to multiply b by 4. You made the same mistake in Line 2 (and then dropped q in the final equation).

But you never solved the system for p and q!

 

[HallsofIvy]

The values for p and q represent the equilibrium point. As related to the troupe’s fundraiser, what does the equilibrium point represent?

The equilibrium point represents the two lines meeting, meaning when they have the same demands.

Actually, only one of the equations refers to "demand". The other refers to "supply" so they can't "have the same demand"!
Each point on the "demand equation" gives the amount people want to by for a given price. each point on the "supply equation" gives the amount that will be supplied at that given price. At the equilibrium point, which is where the two lines cross, "supply" and "demand" will be the same at that price.

What happens when the quantity is above the equilibrium point?
When the quantity is above point that means the price is higher as well as the shirts. People won’t get enough shirts so they won’t be able to buy.

I have no idea what "the price is higher as well as the shirts" means! If the quantity is above the equilibrium point, that means that too many shirts are being produced at that price. People won't buy all of the shirts, the opposite of what you are saying. So either the quantity produced will be lowered or the price will be lowered so people will buy more.

What happens when the quantity is below the equilibrium point?
When the quantity is below the point people will be able to buy as many shirts because the price is low.

Again, you have this exactly backwards! If the quantity is below the equilibrium point, not enough are being produced to sell all at that price. Either the number being produced will be increased or the price will be increased.