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### Question 3:
Ms. Delley has 144 students and is traveling with small vans and large vans. A small van holds 8 people, and a large van holds 12 people. We need to write an equation in standard form that models the possible combinations of small vans and large vans to accommodate all 144 students.

#### Let:
- $ x $ = the number of small vans
- $ y $ = the number of large vans

The total number of students transported is the sum of the students in the small vans and large vans. This gives the equation:
\[
8x + 12y = 144
\]

This is the required equation in standard form.

### Question 5:
Holly earns money at a coffee shop. After two days, she earned $42.50, and after five days, she earned $106.25. We need to find the equation that models her earnings.

#### Let:
- $ y $ = the total amount of money Holly earned after $ x $ days.

First, find the slope (rate of earnings per day). The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where:
- $ (x_1, y_1) = (2, 42.50) $
- $ (x_2, y_2) = (5, 106.25) $

\[
m = \frac{106.25 - 42.50}{5 - 2} = \frac{63.75}{3} = 21.25
\]

So, Holly earns $21.25 per day. Now, using the point-slope form $ y - y_1 = m(x - x_1) $ with $ (x_1, y_1) = (2, 42.50) $:
\[
y - 42.50 = 21.25(x - 2)
\]
Simplifying:
\[
y - 42.50 = 21.25x - 42.50
\]
\[
y = 21.25x
\]
Thus, the equation is:
\[
y = 21.25x
\]
This equation represents the amount of money Holly earned after $ x $ days.

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Would you like further details or explanations on any part of this? Here are five related questions for practice:

1. How many small vans would be needed if no large vans were used to transport the 144 students?
2. If Ms. Delley used 5 large vans, how many small vans would she need to transport the remaining students?
3. What would be Holly's total earnings after 10 days of work?
4. If Holly worked for 7 days, how much more would she have earned compared to after 5 days?
5. How would the equation for Holly’s earnings change if she got a raise and earned $25 per day?

**Tip:** When solving word problems, carefully define variables based on the given context to make your equations clear.

Ms. Delley is taking her class on a trip to the public library. They can travel in small and large vans. A small van holds 8 people, and a large van holds 12 people. Ms. Delley has 144 students in her class. Write an equation in standard form that models the possible combinations of small vans and large vans the class could fill. Also, Holly started working at a coffee shop. After two days, she had earned a total of $42.50. After five days, she had earned a total of $106.25. Which equation models the amount of money Holly earned, y, after x days?

Learn how to model real-life situations using linear equations. Solve problems involving van capacities with Ms. Delley's 144 students and determine Holly's earnings from working in a coffee shop. This guide covers key concepts such as slope, point-slope form, and standard form equations. Ideal for students in Grades 7-9.

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