SOLUTION: Use the given information to analyze what happened with the fundraiser. When the fundraiser began, 600 people wanted to purchase the dance troupe’s T-shirts at $12 per T-shirt,

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Use the given information to analyze what happened with the fundraiser. When the fundraiser began, 600 people wanted to purchase the dance troupe’s T-shirts at $12 per T-shirt,       Log On


   



Question 1011765: Use the given information to analyze what happened with the fundraiser.
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.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Demand:
When p=12, q=600.
When p=13, q=600-50=550.
So then the slope is,
m%5Bd%5D=%28550-600%29%2F%2813-12%29=-50
Using the point-slope form of a line,
q-600=-50%28p-12%29
q-600=-50p%2B600
q=-50p%2B1200
.
.
.
Supply:
When p=9.75, q=600-210=390
When p=10.75, q=390%2B40=430
So then the slope is,
m%5Bs%5D=%28430-390%29%2F%2810.75-9.75%29=40%2F1=40
And similarly,
q-390=40%28p-9.75%29
q-390=40p-390
q=40p