Writing systems of linear equations

Question

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 1

Demand is a function of price, or demand DEPENDS on price.

($12, 600) <--- 600 shirts sold at $12

($9.75, 810) <--- the supply was short by 210, which makes it 810

For every $1 increase in price the demand decreases by 50, so the slope is -50

For every $1 increase in price the supply increases by 40, so the slope is +40

Demand line is y = -50x + b

600 = -50*12 + b

600 = -600 + b

b = 1200

y = -50x + 1200

The supplhy line is y = 40x + b

810 = 50*9.75 + b

810 = 487.50 + b

= 322.50

y = 40x + 322.50

Q = -50p + 1200 is the demand

Q = 40p + 322.50 is the supply

the equilibrium price is -50p + 1200 = 40p + 322.50

1200 - 322.50 = 90p

p = 9.75

9.75 is the equilibrium price