Writing Linear Equations from Word Problems - Free Printable

It looks like you've uploaded a worksheet titled "Writing Linear Equations from Contexts", which contains several word problems that require setting up linear equations based on real-world situations. Since I can't view images directly, I'll solve and explain each problem based on the text you've provided.

Let’s go through each problem one by one:

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1. A local gas pump charges $1.05 for a regular gallon and an extra 3.5 cents per pumping. Write an equation that models the total cost (C) of filling up your car with g gallons.

Step-by-step:
- The base price per gallon is $1.05.
- There's an extra charge of $0.035 per gallon (since 3.5 cents = $0.035).
- So, the total cost per gallon is:
$$
1.05 + 0.035 = 1.085 \text{ dollars per gallon}
$$
- If you buy $ g $ gallons, the total cost $ C $ is:
$$
C = 1.085g
$$

✔ Answer:
$$
\boxed{C = 1.085g}
$$

> Note: This assumes the "extra 3.5 cents per pumping" applies per gallon — which is standard interpretation in such contexts. If it were a flat fee per pump (e.g., $0.035 per transaction), the equation would be different, but since it says "per pumping" and relates to gallons, we assume it's per gallon.

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2. The waterpark's lunch stand holds 10,000 gallons of water. On a hot summer day, the water evaporates at a rate of 150 gallons per hour. Write an equation that models the amount of water, w, and the time, t (in hours).

Step-by-step:
- Initial amount of water: 10,000 gallons.
- Water decreases at 150 gallons per hour.
- After $ t $ hours, the amount lost is $ 150t $.
- So, remaining water $ w $ is:
$$
w = 10,000 - 150t
$$

✔ Answer:
$$
\boxed{w = 10,000 - 150t}
$$

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3. Gas prices in Sacramento are approximately $3.75 per gallon. Write an equation that models the cost, c, and gallons, g.

Step-by-step:
- Price per gallon: $3.75
- For $ g $ gallons, total cost $ c $ is:
$$
c = 3.75g
$$

✔ Answer:
$$
\boxed{c = 3.75g}
$$

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4. Operating costs at a local business are $360 per day. On average, the business makes $12 per customer. Write an equation that models the profit, p, and the number of customers, c. Then find how many customers would have to visit the store to make $600 in profit.

Step-by-step:
- Fixed daily cost: $360
- Revenue per customer: $12
- Total revenue from $ c $ customers: $ 12c $
- Profit $ p $ = Revenue – Cost
$$
p = 12c - 360
$$

Now, set $ p = 600 $ and solve for $ c $:
$$
600 = 12c - 360
$$
Add 360 to both sides:
$$
960 = 12c
$$
Divide by 12:
$$
c = 80
$$

✔ Answer:
- Equation: $ \boxed{p = 12c - 360} $
- Number of customers needed: $ \boxed{80} $

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5. Julie rents a bike for a ride. The local rental company charges her a flat rate of $20, plus $10 per hour for the bike. She writes the equation: $ y = 20x + 10 $. Is this equation correct? Explain.

Step-by-step:
- Flat rate: $20 (fixed cost)
- Per hour charge: $10 per hour
- Let $ x $ = number of hours
- Then total cost $ y $ should be:
$$
y = 10x + 20
$$
- But Julie wrote: $ y = 20x + 10 $

This is incorrect because:
- The coefficient of $ x $ should be 10 (cost per hour), not 20.
- The constant term should be 20 (flat fee), not 10.

✔ Answer:
- No, the equation is not correct.
- The correct equation is: $ \boxed{y = 10x + 20} $
- Julie swapped the fixed cost and hourly rate.

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6. Create your own context and write an equation to go along with it.

Example:
- Context: A taxi service charges a $5 pickup fee and $2 per mile driven.
- Let $ m $ = number of miles
- Let $ C $ = total cost
- Then:
$$
C = 2m + 5
$$

✔ Answer (example):
- Context: A pizza place charges a $10 delivery fee and $12 per pizza.
- Equation: $ \boxed{C = 12p + 10} $, where $ p $ = number of pizzas, $ C $ = total cost.

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✔ Summary of Answers:

1. $ C = 1.085g $
2. $ w = 10,000 - 150t $
3. $ c = 3.75g $
4. $ p = 12c - 360 $; 80 customers
5. No, correct equation is $ y = 10x + 20 $
6. Example: $ C = 12p + 10 $ (pizza delivery)

Let me know if you'd like these formatted as a PDF or need help graphing any of them!