SOLUTION: Could you please help me by providing a step-by-step answer to the following equation: A museum offers excursions at $12.00 per ticket if 100 or fewer tickets are purchased. For

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Question 465504: Could you please help me by providing a step-by-step answer to the following equation:
A museum offers excursions at $12.00 per ticket if 100 or fewer tickets are purchased. For each ticket over 100, the price is reduced by 10 cents. How many tickets will lead to a maximum income? (Solve using a quadratic formula.)
I'm familiar with the quadratic formula and how to use it, but I'm not quite sure how to approach this particular word problem.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of tickets over 100.
==> price of ticket is 12 - 0.10x
==> number of tickets is 100 + x
==> Income, or revenue, is %28100+%2B+x%29%2812+-+0.10x%29+=+1200+%2B+2x+-+0.10x%5E2. Since the the coefficient of x%5E2 is negative (-0.10), there is an absolute maximum (parabola faces downward). The x-value that gives the maximum income is -b%2F%282a%29+=+-2%2F%282%2A-0.10%29+=+2%2F0.20+=+10. Hence 100 + 10 = 110 tickets must be sold to get maximum income.