https://file.aiquickdraw.com/mathbot/file/1729627999369hwzuvyax.jpg

We need to find the largest number of laptops that can be bought for the same price as 32 Halton laptops.

### Step 1: Calculate the total price for 32 Halton laptops.
- **Base price of a Halton laptop**: £319
- **Discount for 31-40 laptops**: 8%

The discounted price for each Halton laptop is:
\[
319 \times (1 - 0.08) = 319 \times 0.92 = £293.48
\]
So, the total price for 32 Halton laptops is:
\[
32 \times 293.48 = £9,391.36
\]

### Step 2: Calculate the number of laptops from each brand that can be bought for £9,391.36

#### Fox Laptops:
- **Base price**: £249
- **Discount for 41-50 laptops**: 20%
\[
249 \times (1 - 0.20) = 249 \times 0.80 = £199.20
\]
The number of Fox laptops that can be bought is:
\[
\frac{9391.36}{199.20} \approx 47.15 \text{ laptops}
\]
Thus, 47 Fox laptops can be bought.

#### Masterix Laptops:
- **Base price**: £289
- **Discount for 41-50 laptops**: 19%
\[
289 \times (1 - 0.19) = 289 \times 0.81 = £234.09
\]
The number of Masterix laptops that can be bought is:
\[
\frac{9391.36}{234.09} \approx 40.1 \text{ laptops}
\]
Thus, 40 Masterix laptops can be bought.

#### Preston Laptops:
- **Base price**: £230
- **Discount for 41-50 laptops**: 9%
\[
230 \times (1 - 0.09) = 230 \times 0.91 = £209.30
\]
The number of Preston laptops that can be bought is:
\[
\frac{9391.36}{209.30} \approx 44.88 \text{ laptops}
\]
Thus, 44 Preston laptops can be bought.

#### Vision Laptops:
- **Base price**: £239
- **Discount for 41-50 laptops**: 14%
\[
239 \times (1 - 0.14) = 239 \times 0.86 = £205.54
\]
The number of Vision laptops that can be bought is:
\[
\frac{9391.36}{205.54} \approx 45.68 \text{ laptops}
\]
Thus, 45 Vision laptops can be bought.

### Conclusion:
The largest number of laptops that can be bought for the same price as 32 Halton laptops is **47 Fox laptops**.

Let me know if you'd like further clarification or details!

---

Here are five related questions:
1. How would the number of laptops change if the discount percentage was increased?
2. What would be the cost difference if we bought 40 Halton laptops instead of 32?
3. Can you calculate how many Preston laptops can be bought with a different budget?
4. How would the calculations change if no discounts were applied to any laptop brand?
5. What if the Fox laptops only had a 10% discount—how many could you buy for the same price?

**Tip**: When working with percentage discounts, always apply the percentage as a decimal (e.g., 20% becomes 0.20) to calculate the effective price!

What is the largest number of laptops that can be bought for the same price as 32 Halton laptops?

Explore how to calculate the largest number of laptops that can be purchased for the same price as 32 Halton laptops using percentage discounts. Detailed solution involves calculating discounted prices for various brands and comparing quantities. Suitable for high school students, Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation