Basic Algebra Worksheets - Free Printable

Let's solve each of these algebra word problems step by step and write the correct algebraic expressions for each. We’ll also identify which one is the "trick problem" that doesn’t actually require algebra.

---

1) In a stable, there are h horses. 6 of them are taken out into the yard to exercise. How many are left in the stable?

- Total horses: h
- Horses taken out: 6
- Remaining: $ h - 6 $

✔ Answer: $ h - 6 $

---

2) There are c cyclists in a cycle race. $ \frac{3}{4} $ of the cyclists finish the race. How many cyclists did not finish?

- Total cyclists: c
- Finished: $ \frac{3}{4}c $
- Did not finish: $ c - \frac{3}{4}c = \frac{1}{4}c $

✔ Answer: $ \frac{1}{4}c $

---

3) There are 56 people on a bus. t people get off at the next stop and 3 more people get on. How many people are on the bus now?

- Start: 56
- Get off: t
- Get on: 3
- Final count: $ 56 - t + 3 = 59 - t $

✔ Answer: $ 59 - t $

---

4) In a class of 30 children, g children come to school by bus. What fraction of the class come by bus?

- Total children: 30
- By bus: g
- Fraction: $ \frac{g}{30} $

✔ Answer: $ \frac{g}{30} $

---

5) In a class of c children, 16 have blue eyes. What fraction of the class have blue eyes?

- Total: c
- Blue eyes: 16
- Fraction: $ \frac{16}{c} $

✔ Answer: $ \frac{16}{c} $

---

6) There are b people on a bus. At the next stop, 7 people get off and 10 more get on. How many more people are on the bus now?

- Start: b
- After: $ b - 7 + 10 = b + 3 $
- But the question asks: How many more? → Difference from original

So: $ (b + 3) - b = 3 $

➡️ This is 3, a constant — no variable needed!

✔ Answer: $ 3 $

> 🔍 This is the "trick problem"! It does not need algebra because the answer is always 3 more people, regardless of b.

---

7) I cut a long piece of wood into 50cm pieces. I manage to cut w pieces of wood, and there is 20cm left over. How long was the wood to start with?

- Each piece: 50 cm
- Number of pieces: w
- Total used: $ 50w $
- Leftover: 20 cm
- Original length: $ 50w + 20 $

✔ Answer: $ 50w + 20 $

---

8) I have c chocolates which I share equally between my 5 friends. How many do they each get?

- Total chocolates: c
- Shared among 5 friends
- Each gets: $ \frac{c}{5} $

✔ Answer: $ \frac{c}{5} $

---

9) I have 5 pens already. I am given 2 packs of pens. Each pack contains t pens. How many pens do I have now?

- Already have: 5
- 2 packs × t pens per pack = $ 2t $
- Total: $ 5 + 2t $

✔ Answer: $ 5 + 2t $

---

10) There are d deer and p pheasants in the woods. How many legs in total?

- Deer have 4 legs → $ 4d $
- Pheasants have 2 legs → $ 2p $
- Total legs: $ 4d + 2p $

✔ Answer: $ 4d + 2p $

---

✔ Final Answers:

| Problem | Algebraic Expression |
|--------|----------------------|
| 1) | $ h - 6 $ |
| 2) | $ \frac{1}{4}c $ |
| 3) | $ 59 - t $ |
| 4) | $ \frac{g}{30} $ |
| 5) | $ \frac{16}{c} $ |
| 6) | $ 3 $ ← Trick problem! No algebra needed |
| 7) | $ 50w + 20 $ |
| 8) | $ \frac{c}{5} $ |
| 9) | $ 5 + 2t $ |
| 10) | $ 4d + 2p $ |

---

🎯 The Trick Problem:

👉 Problem #6 is the trick one because the number of additional people on the bus is always 3, no matter how many were there originally. So it’s just a number, not an expression involving variables.

---

Let me know if you'd like this formatted as a printable sheet or want explanations for any specific steps!