The Atlanta United youth soccer team is planning a barbeque fundraiser. The catering company charges $2.75 per person plus a flat fee of $250. The club can only spend $500 for food service.

A)

B) 90 People

C) No.

Step-by-step explanation:

We know that the catering company charges $2.75 per person plus a flat fee of $250.

And the club can only afford to spend $500.

Part A)

Let the amount of people be p.

We know that we have a flat fee of $250. It is also $2.75 per person p.

So, we can write the following expression:

The club can only spend $500. Therefore, the cost of the fee and for p people must be 500 or below.

In other words, our sign is less than or equal to:

We cannot spend more than 500, but we can spend exactly 500.

Therefore, our inequality is:

Part B)

To determine the maximum amount of people, we can solve our inequality for p.

So, we have:

Subtract 250 from both sides:

Divide both sides by 2.75:

Our answer is about 90.9090...

Since our p is people, we must round down.

So, the maximum amount of people we can serve is 90 people.

Part C)

As determined by the previous part, the maximum amount of people we can serve is 90 people.

100 is greater than 90, so we cannot afford to serve 100 people.

Mathematically, let’s substitute 100 for our p in our inequality. This yields:

Multiply and add:

525 is not less than 500.

Therefore, we cannot afford to accommodate 100 people. The maximum is 90.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x