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

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) (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 . Since the the coefficient of is negative (-0.10), there is an absolute maximum (parabola faces downward). The x-value that gives the maximum income is . Hence 100 + 10 = 110 tickets must be sold to get maximum income.
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