Finding the Best Buy Using Ratio - Mr-Mathematics.com - Free Printable

Let's solve both questions step by step using ratio notation to compare value for money. The goal is to find the price per gram (or price per unit weight) for each option and then compare them.

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✔ Question 1: Peanut Butter

You can buy peanut butter in two sizes:

- Jar A: 450 g for £1.44
- Jar B: 340 g for £1.16

We want to determine which jar gives better value for money — that is, which one costs less per gram.

#### Step 1: Find the cost per gram for each jar

We use ratio notation:
$$
\text{Cost per gram} = \frac{\text{Price}}{\text{Weight}}
$$

##### Jar A:
$$
\frac{£1.44}{450\ \text{g}} = \frac{1.44}{450} = 0.0032\ \text{£/g}
$$

##### Jar B:
$$
\frac{£1.16}{340\ \text{g}} = \frac{1.16}{340} ≈ 0.00341\ \text{£/g}
$$

#### Step 2: Compare the values

- Jar A: £0.0032 per gram
- Jar B: £0.00341 per gram

Since Jar A has a lower cost per gram, it is the better value.

✔ Answer: Jar A is better value for money.

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✔ Question 2: Flour

Flour is sold in three sizes:

- Small: 750 g for £0.85
- Medium: 1 kg (1000 g) for £1.05
- Large: 2.4 kg for £2.04

We'll again calculate the cost per gram for each.

#### Step 1: Convert all weights to grams (already done)

Now compute cost per gram:

##### Small:
$$
\frac{£0.85}{750\ \text{g}} = \frac{0.85}{750} ≈ 0.001133\ \text{£/g}
$$

##### Medium:
$$
\frac{£1.05}{1000\ \text{g}} = \frac{1.05}{1000} = 0.00105\ \text{£/g}
$$

##### Large:
$$
\frac{£2.04}{2400\ \text{g}} = \frac{2.04}{2400} = 0.00085\ \text{£/g}
$$

#### Step 2: Compare

- Small: £0.001133/g
- Medium: £0.00105/g
- Large: £0.00085/g

The large size has the lowest cost per gram, so it’s the best value.

✔ Answer: The large size (2.4 kg for £2.04) is the best value for money.

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📌 Summary

| Product | Size | Price | Weight | Cost per gram | Value Rank |
|--------|------|-------|--------|----------------|------------|
| Peanut Butter | A | £1.44 | 450g | £0.0032 | Better |
| Peanut Butter | B | £1.16 | 340g | £0.00341 | Worse |
| Flour | Small | £0.85 | 750g | £0.001133 | Third |
| Flour | Medium | £1.05 | 1000g | £0.00105 | Second |
| Flour | Large | £2.04 | 2400g | £0.00085 | Best |

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✔ Final Answers:

- Question 1: Jar A is better value.
- Question 2: Large size is the best value.

💡 Tip: Always use unit rate (price per gram) to compare value when quantities differ. This is the core of ratio-based problem solving!