Algebra Word Problems Sheet 3 (UK version) - Answers

It looks like you've uploaded an answer key for "Algebra Word Problems Sheet 3 (UK version)" from Math-Salamanders.com. The sheet contains 9 algebraic word problems, each with a corresponding expression or formula as the answer.

However, since this is the answer sheet, not the original problem sheet, I’ll go through each question and explain how to arrive at the given answers, so you can understand the reasoning behind them.

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🔍 Problem-by-Problem Explanation

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#### 1) A chicken weighs t lb. It needs to be cooked for 20 minutes per lb plus an extra 15 minutes. What is the total cooking time?

- Answer: $ 20t + 15 $ minutes

✔ Explanation:
- For each pound (t), it takes 20 minutes → $ 20 \times t = 20t $
- Plus an extra 15 minutes regardless of weight
- Total time = $ 20t + 15 $

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#### 2) I put £100 in a savings account at v% yearly interest. How much money will I have in my account at the end of a year?

- Answer: £100 + v

⚠️ Note: This is not fully accurate unless we assume v is the interest amount in pounds, not a percentage.

But if v% means v percent, then:
- Interest = $ \frac{v}{100} \times 100 = v $ pounds
- So total after one year = $ 100 + v $

✔ So yes, the answer £100 + v is correct if v is the interest amount in pounds (i.e., v% of £100 = £v).
This assumes simple interest and that v is interpreted as the amount, not the rate.

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#### 3) I get £m for my birthday. I spend half the money, but get given an extra £50. How much money do I have now?

- Answer: £$ \frac{1}{2}m + 50 $

✔ Explanation:
- Start with: £m
- Spend half: $ \frac{1}{2}m $
- Left with: $ \frac{1}{2}m $
- Then receive £50 → Add 50
- Final amount: $ \frac{1}{2}m + 50 $

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#### 4) A calculator costs £d. A school buys 90 calculators, and gets a £100 discount for bulk purchasing. How much did the school spend?

- Answer: £$ 90d - 100 $

✔ Explanation:
- Cost of 90 calculators: $ 90 \times d = 90d $
- Subtract £100 discount: $ 90d - 100 $

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#### 5) A square has sides of t cm. What is the area of the square?

- Answer: $ t^2 $ cm²

✔ Explanation:
- Area of a square = side × side = $ t \times t = t^2 $

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#### 6) A rectangle measures w inches by h inches. What is the perimeter of the rectangle?

- Answer: $ 2(w + h) $ or $ 2w + 2h $ inches

✔ Explanation:
- Perimeter = sum of all sides = $ w + h + w + h = 2w + 2h $
- Factorized: $ 2(w + h) $

Both forms are correct.

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#### 7) I have £g. I spend half my money on a console game and £20 on a controller. How much money do I have left?

- Answer: £$ \frac{1}{2}g - 20 $

✔ Explanation:
- Start with: £g
- Spend half on game: $ \frac{1}{2}g $
- Remaining: $ g - \frac{1}{2}g = \frac{1}{2}g $
- Then spend £20 on controller → subtract 20
- Final amount: $ \frac{1}{2}g - 20 $

> ⚠️ Note: This assumes the £20 is spent after buying the game.

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#### 8) I need to buy p pencils. I buy 4 packs of 7 pencils, but I still need a few more. How many pencils did I buy?

- Answer: $ 4 \times 7 = 28 $ pencils (trick question)

✔ Explanation:
- The question asks: "How many pencils did I buy?"
- You bought 4 packs × 7 pencils = 28 pencils
- Even though you still need more, the question is only about what was bought, not how many are needed.
- So the answer is 28, regardless of p.
- That’s why it's a trick question: it tries to mislead you into thinking you need to use 'p'.

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#### 9) A car travels 120 miles in h hours. What is the average speed in miles per hour?

- Answer: $ \frac{120}{h} $

✔ Explanation:
- Average speed = Total distance ÷ Time
- $ \frac{120 \text{ miles}}{h \text{ hours}} = \frac{120}{h} $ mph

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✔ Summary of Key Concepts

| Concept | Used In |
|-------|--------|
| Multiplication & Addition | #1, #4 |
| Percentages (simple interest) | #2 |
| Fractions & Money | #3, #7 |
| Area of Square | #5 |
| Perimeter of Rectangle | #6 |
| Trick Question Logic | #8 |
| Speed = Distance ÷ Time | #9 |

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📝 Final Notes:

- These are algebraic expressions, not equations to solve numerically — they represent relationships.
- The answers are expressions, not numbers.
- Some questions test reading comprehension (like #8).
- Always pay attention to what is being asked — e.g., “how much did I buy?” vs. “how many do I still need?”

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Let me know if you'd like the original problem sheet or help turning these into practice exercises!