Question

a parent group for a local kindergarten is investigating different possibilities for a celebration at the end of the school year. a local party supply store will charge $410 to rent a ball pit and trampoline for the entire day. a local company will supply transportation at a cost of $25 per person. each person attending will be charged 35 dollars, which includes food, games, and round - trip transportation. the board of education has promised the parent group $150 to defray costs.
defines units for the cost of the trip and the amount of money collected to pay for the trip. enter a variable for the number of people and use this variable to write expressions for the cost of the trip and the amount of money collected to pay for the trip.
if fourteen people attend, what is the total cost of the event and how much will be collected to pay for it?

1. how many people need to make the trip in order to break even, according to the algebraic model?

(and there is a table with columns: quantity name, unit, expression, question 1, question 2, question 3, question 4; and a graph with dollars on the y - axis with values 600, 900, 1200, 1500 and an arrow on the x - axis)

Explanation:

Step1: Identify the total cost expression

The cost for the trip is given by the expression \( 410 + 25x \), where \( x \) is the number of people.

Step2: Substitute \( x = 14 \) into the cost expression

We need to find the total cost when 14 people attend. So substitute \( x = 14 \) into \( 410 + 25x \).
First, calculate \( 25\times14 \): \( 25\times14 = 350 \)
Then, add 410 to the result: \( 410+350 = 760 \)
Wait, but there is also the amount collected which is \( 35x + 150 \). Wait, maybe I misread. Wait, the problem says "the total cost of the event and how much will be collected to pay for it" when 14 people attend. Wait, let's re - examine.

Wait, the cost for the trip (from the party supply etc.) is \( 410+25x \), and the amount collected (from each person paying 35 and the board giving 150) is \( 35x + 150 \).

Wait, when \( x = 14 \):

For the cost:

Step1: Calculate \( 25x \) when \( x = 14 \)

\( 25\times14=350 \)

Step2: Add 410 to it

\( 410 + 350=760 \)

For the amount collected:

Step1: Calculate \( 35x \) when \( x = 14 \)

\( 35\times14 = 490 \)

Step2: Add 150 to it

\( 490+150 = 640 \)

Wait, but maybe the question is about the total cost of the event (cost + collected?) No, the problem says "the total cost of the event and how much will be collected to pay for it" when 14 people attend.

Wait, the cost of the trip (from the party supply) is \( 410 + 25x \), and the amount collected to pay for the trip is \( 35x+150 \).

When \( x = 14 \):

Cost: \( 410+25\times14=410 + 350=760 \) dollars.

Amount collected: \( 35\times14+150=490 + 150 = 640 \) dollars.

But maybe the question is just about the amount collected? Wait, the original problem says "If fourteen people attend, what is the total cost of the event and how much will be collected to pay for it."

Wait, maybe I made a mistake. Let's check the table. In the table, for Question 1, when \( x = 14 \), let's see the amount collected expression is \( 35x + 150 \).

So for \( x = 14 \):

\( 35\times14+150=490 + 150=640 \)

And the cost is \( 410+25\times14 = 410+350 = 760 \)

But maybe the question is about the amount collected to pay for the trip. Let's assume that we need to find the amount collected when \( x = 14 \) using the expression \( 35x + 150 \).

Step1: Substitute \( x = 14 \) into \( 35x+150 \)

First, calculate \( 35\times14 \): \( 35\times14=(30 + 5)\times14=30\times14+5\times14 = 420+70 = 490 \)

Step2: Add 150 to 490

\( 490+150 = 640 \)

Answer:

If we are calculating the amount collected to pay for the trip when 14 people attend, the total amount collected is \(\boldsymbol{640}\) dollars. If we are calculating the total cost of the trip, it is \(\boldsymbol{760}\) dollars. (Based on the context, if we consider the amount collected to pay for it, the answer is 640)