Can you me with this question ? 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."

Demand: q = -50p + 1200

Supply: q = 40p

Step-by-step explanation:

First let's define our variables.

q = quantity of T-shirts

p = price

We 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 + 600

q = -50p + 1200

Similarly, 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 - 390

q = 40p

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step-by-step explanation:

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