Math worksheet for expressing equations from word problems.

Let's solve each problem step by step. The goal is to write an equation that expresses the relationship between two variables: usually total cost (t) or total quantity (t) and the number of items (n, b, p, etc.). These are all proportional relationships, so we'll use the form:

$$
t = r \cdot x
$$

Where:
- $ t $ = total amount (cost, weight, distance, etc.)
- $ r $ = rate per unit (price per ticket, weight per block, etc.)
- $ x $ = number of units (tickets, blocks, etc.)

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1) Carnival Tickets

- Cost for 71 tickets = $91.59
- Find cost per ticket:
$$
\frac{91.59}{71} = 1.29
$$
- So, cost per ticket = \$1.29
- Equation:
$$
t = 1.29n
$$

✔ Answer: $ t = 1.29n $

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2) Birdhouses from Nails

- 26 boxes → 234.00 birdhouses
- Rate per box:
$$
\frac{234}{26} = 9
$$
- So, 9 birdhouses per box of nails
- Equation:
$$
t = 9b
$$

✔ Answer: $ t = 9b $

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3) Concrete Blocks

- 22 blocks → 332.86 kg
- Weight per block:
$$
\frac{332.86}{22} = 15.13
$$
- So, each block weighs 15.13 kg
- Equation:
$$
t = 15.13b
$$

✔ Answer: $ t = 15.13b $

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4) Oranges

- 16 bags → \$47.52
- Price per bag:
$$
\frac{47.52}{16} = 2.97
$$
- So, each bag costs \$2.97
- Equation:
$$
t = 2.97b
$$

✔ Answer: $ t = 2.97b $

---

5) Beef Jerky

- 35 pounds → \$448.00
- Cost per pound:
$$
\frac{448}{35} = 12.80
$$
- So, \$12.80 per pound
- Equation:
$$
t = 12.80p
$$

✔ Answer: $ t = 12.80p $

---

6) Vanessa’s Travel

- 55.68 km in 64 minutes
- Speed (km per minute):
$$
\frac{55.68}{64} = 0.87
$$
- So, 0.87 km per minute
- Equation:
$$
t = 0.87m
$$

✔ Answer: $ t = 0.87m $

---

7) Science Books

- 12 books → \$428.40
- Cost per book:
$$
\frac{428.40}{12} = 35.70
$$
- So, \$35.70 per book
- Equation:
$$
t = 35.70b
$$

✔ Answer: $ t = 35.70b $

---

8) Lemons for Lemonade

- 42 bottles → 378 lemons
- Lemons per bottle:
$$
\frac{378}{42} = 9
$$
- So, 9 lemons per bottle
- Equation:
$$
t = 9b
$$

✔ Answer: $ t = 9b $

---

9) Phone Cases

- 17 cases → \$48.62
- Money per case:
$$
\frac{48.62}{17} = 2.86
$$
- So, \$2.86 per case
- Equation:
$$
t = 2.86c
$$

✔ Answer: $ t = 2.86c $

---

10) Candy Bars Fundraiser

- 26 candy bars → \$66.56
- Price per bar:
$$
\frac{66.56}{26} = 2.56
$$
- So, \$2.56 per candy bar
- Equation:
$$
t = 2.56b
$$

✔ Answer: $ t = 2.56b $

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✔ Final Answers:

1. $ t = 1.29n $
2. $ t = 9b $
3. $ t = 15.13b $
4. $ t = 2.97b $
5. $ t = 12.80p $
6. $ t = 0.87m $
7. $ t = 35.70b $
8. $ t = 9b $
9. $ t = 2.86c $
10. $ t = 2.56b $

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Let me know if you'd like this formatted as a printable answer sheet!