Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $
25. The venue has the capacity to hold 400 people. The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school:
What is the minimum number of at-the-door tickets she needs to sell to make her goal?
A,333
B.334
C.66
D.67
What is the minimum number of at-the-door tickets she needs to sell to make her goal?
A,333
B.334
C.66
D.67
2 answers:
Answer:
D. 67
Step-by-step explanation:
To help me see the region we needed to look at, I wrote the inequalities out.
Let x be number of pre-sale tickets and y be the number of at-the-door tickets as your graph suggests.
So one of the inequalities about number of where the other one is about cost.
You are given x+y is no more than 400 or x+y<=400 (the top line graphed in your picture is x+y=400).
You are given 10x+25y is at least 5000 or 10x+25y>=5000 (the bottom line graphed in your picture).
I solved both of these for y.
x+y<=400
Subtract x on both sides giving y<=-x+400 (shaded below line because of the y< part).
10x+25y>=5000
Subtract 10x on both sides:
25y>=-10x+5000
Divide both sides by 25:
y>=-2/5 x+200 (shaded above the line because of y> part).
The region we should then be looking at is:
Let's look at the points (0,400), (0,200), and finally (333,67).
Cost=10x+25y
Let's plug in
Cost=10(0)+25(400)=10000
Cost=10(0)+25(200)=5000 (can we go lower than 200)
Cost=10(333)+25(67)=5005 (our y is lower 200 so far this is the winner)
Cost 10(334)+25(66)=4990 (didn't meet the 5000 dollar requirement)
67 D.
(Also if you look at the graph 66 would not be included in the shaded region; it would be too low)
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