MEDAL FOR HELP! SWAG BELOW!

A school fundraiser is selling a custom design t-shirt. Their revenues are modeled by the quadratic equation, R = 0.03t + 550, where R is revenue in dollars for the sale of t number of t-shirts. The expenses, E, for printing and selling t-shirts are given by the linear equation E = 250 + 3.50t

If 75 students have already paid for a shirt, approximately how many more do they need to sell in order to break even

A 25 t-shirts
B 57 t shirts
C 102 t-shirts
D 177 t-shirts

Question

MEDAL FOR HELP! SWAG BELOW!

A school fundraiser is selling a custom design t-shirt.  Their revenues are modeled by the quadratic equation, R = 0.03t + 550, where R is revenue in dollars for the sale of t number of t-shirts. The expenses, E, for printing and selling t-shirts are given by the linear equation E = 250 + 3.50t

If 75 students have already paid for a shirt, approximately how many more do they need to sell in order to break even

A 25 t-shirts
B 57 t shirts
C 102 t-shirts
D 177 t-shirts

anonymous · Answer

@dan815 @whpalmer4

anonymous · Answer

The answer is C, i know that but I want to know how.  Can someone help explain :)

anonymous · Answer

@satellite73

anonymous · Answer

solve $$0.03t + 550=250 + 3.50t $$ then subtract $75$ from the answer

anonymous · Answer

its supposed to be .03t^2 my bad

whpalmer4 · Answer

Okay, so the corrected revenue function is apparently$$R = 0.03t^2 + 550$$whereas expenses are given by $$E = 250 + 3.50t$$
The break-even point is where revenues equal expenses:
$$R=E$$$$0.03t^2+550=250+3.50t$$
Solve that for $t$ and subtract $75$ to account for the $75$ shirts already sold.  Problem I have with all of this is that your equations must not be copied correctly, as those two functions are never equal for real values of $t$.  Solving @satellite73's version of the equations doesn't get you a working answer either.  I'd appreciate seeing the correct problem, out of curiosity if nothing else!