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# help with problem

A school band is planning an honoree and fundraiser banquet To encourage attendance a \$200 cash door prize will be given The caterer has offered them two choices for the meal Plan A The caterer will charge 7.25 per meal and the band will charge \$18 for a ticket to the banquet, and plan B the caterer will charge \$8 per meal and the choir will charge \$20 per ticket. The band plans of making \$800 with the banquet. Determine which meal plan the band should choose. explain the reason for your decision

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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Let x = the number of people attending the banquet.
Let y = the funds the school band makes from the banquet

The costs are \$200 for the door prize and the meal cost per person attending (meal cost*x).  Revenues are the ticket prices per person attending (ticket price*x).  The net revenue (y=Revenue-Costs) equations are:

For plan A:  yA = (\$18)x- (\$7.25)x - \$200 = (\$10.75)x - \$200

For plan B:  yB = (\$20)x - (\$8)x - \$200 = (\$12)x - \$200

To make their goal of \$800 with plan A:

\$800 = (10.75)x - 200
1000 = (10.75)x

93 people ≅ x          They need 93 people to attend

To make their goal of \$800 with plan B:

\$800 = 12x - 200
1000 = 12x

84 people ≅ x                 They need 84 people to attend

Plan B allows the band to reach its goal with nine fewer people attending the banquet.  For any given value of x, plan B will return more net revenue than plan A (since its slope is steeper).  So with the information provided, the answer would seem to be plan B. In the real-world, however, as the ticket cost rises, the number of people willing to buy tickets decreases.  So we aren't sure if the extra \$2 per ticket for plan B will scare away more than 9 potential ticket buyers.  To truly solve this problem, we need to know how attendance is affected by ticket cost.