Math worksheet with linear equation word problems and solutions.

Let's go through each of the problems in your image and solve them step-by-step, checking for accuracy and explaining the reasoning.

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Problem 6: School Play Tickets

> Tickets at a school play cost $4 in advance or $5 at the door. Total ticket sales were $440. If no tickets were sold in advance, how many were sold at the door?

#### Given:
- Advance ticket price = $4
- Door ticket price = $5
- Total sales = $440
- No tickets sold in advance → $x = 0$

Let:
- $ x $ = number of tickets sold in advance
- $ y $ = number of tickets sold at the door

Equation:
$$
4x + 5y = 440
$$

Since $ x = 0 $ (no advance sales):
$$
4(0) + 5y = 440 \\
5y = 440 \\
y = \frac{440}{5} = 88
$$

✔ Answer: $ \boxed{88} $ tickets were sold at the door.

✔️ Your solution is correct.

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Problem 7: Karen’s Piggy Bank

> Karen has dimes and quarters. Total value = $11.40. She has 36 quarters. Find number of dimes.

Let:
- $ x $ = number of dimes
- $ y $ = number of quarters = 36

Value:
- Dime = $0.10
- Quarter = $0.25

Equation:
$$
0.10x + 0.25y = 11.40
$$

Substitute $ y = 36 $:
$$
0.10x + 0.25(36) = 11.40 \\
0.10x + 9 = 11.40 \\
0.10x = 11.40 - 9 = 2.40 \\
x = \frac{2.40}{0.10} = 24
$$

✔ Answer: $ \boxed{24} $ dimes

✔️ Your solution is correct.

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Problem 8: Oakville High School Marching Band

> Solid gift wrap: $3.50 per roll
> Printed gift wrap: $5 per roll
> Need to earn $2,500
> Sold 325 rolls of printed paper
> Find how many solid rolls must be sold

Let:
- $ x $ = number of solid rolls
- $ y $ = number of printed rolls = 325

Equation:
$$
3.50x + 5y = 2500
$$

Substitute $ y = 325 $:
$$
3.50x + 5(325) = 2500 \\
3.50x + 1625 = 2500 \\
3.50x = 2500 - 1625 = 875 \\
x = \frac{875}{3.50}
$$

Now calculate:
$$
\frac{875}{3.5} = \frac{8750}{35} = 250
$$

✔ Answer: $ \boxed{250} $ solid rolls must be sold

✔️ Your setup was correct, but you stopped mid-calculation. The final answer is 250.

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 6 | 88 tickets sold at the door |
| 7 | 24 dimes |
| 8 | 250 solid rolls |

All your work is correct, except that Problem 8 needs the final division completed.

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🔍 Additional Note: Point & Slope Section (Blurred)

The bottom part says "POINT & SLOPE" but it's blurry. It seems like a separate section about writing equations given a point and slope using the point-slope form:
$$
y - y_1 = m(x - x_1)
$$

If you'd like help with that section once it's clearer, feel free to ask!

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Let me know if you want these problems explained in simpler terms or visualized!