Question

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 for $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 pre-sale tickets she needs to sell to make her goal?

333
66
67

Answer 1

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.

Answer 2

Answer:

67

Explanation:

Let us assume that Anna sells x number of pre-sale tickets and y number of at-the-door tickets.

Since, total capacity of the venue is 400, so we can write x + y = 400 ...... (1)

Now, given that each pre-sale ticket costs $10 and each at-the-door ticket costs $25, and the total funds she needs to raise is $5000

So, we can write 10x + 25y = 5000, ⇒ x + 2.5y = 500 .... (2)

Now, solving equations (1) and (2) we get,  

(2.5 - 1)y = 500 - 400 = 100

⇒ 1.5y = 100

⇒ y = 66.67

Hence, from equation (1) we get, x = 400 - 66.67 = 333.33

Since Y can't be a fraction and it can not be < 66.67 (Otherwise the goal of $5000 can not be achieved)

So, the minimum number of at-the-door ticket she needs to sell to make her goal is 67.