Q:

Can you help me with this question please? I will reward 20 points for best answer. * You don't have to solve the problem for me, I just want to know the formula and how to solve 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."

Accepted Solution

A:
Answer:Demand: q = -50p + 1200Supply: q = 40pStep-by-step explanation:First let's define our variables.q = quantity of T-shirtsp = priceWe know that when p = 12, q = 600.  When p increases by 1, q decreases by 50.  So this is a line with slope -50 that passes through the point (12, 600).  Using point-slope form to write the equation:q - 600 = -50 (p - 12)Converting to slope-intercept form:q - 600 = -50p + 600q = -50p + 1200Similarly, we know that when p = 9.75, q = 600 - 210 = 390.  When p increases by 1, q increases by 40.  So this is a line with slope 40 that passes through the point (9.75, 390).  Using point-slope form to write the equation:q - 390 = 40 (p - 9.75)Converting to slope-intercept form:q - 390 = 40p - 390q = 40p