1. 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.
Accepted Solution
A:
Step-by-step explanation:($12, 600) <--- 600 shirts sold at $12($9.75, 810) <--- the supply was short by 210, which makes it 810For every $1 increase in price the demand decreases by 50, so the slope is -50For every $1 increase in price the supply increases by 40, so the slope is +40Demand line is y = -50x + b 600 = -50*12 + b 600 = -600 + b b = 1200 y = -50x + 1200The supplhy line is y = 40x + b 810 = 50*9.75 + b 810 = 487.50 + b = 322.50 y = 40x + 322.50Q = -50p + 1200 is the demandQ = 40p + 322.50 is the supplythe equilibrium price is -50p + 1200 = 40p + 322.50 1200 - 322.50 = 90p p = 9.759.75 is the equilibrium price (if it's too long or you don't understand, just delete)