For each of two consecutive years cheese prices rose by 10 per cent. At the beginning of the first year 1kg of
cheese cost $5. At the end of the second year how many grams of cheese, to the nearest ten gram, could be
bought for $10?

Let's solve the problem step by step.

### Step 1: Determine the cost of 1 kg of cheese at the end of the first year
The initial price of 1 kg of cheese is $5. At the end of the first year, the price increases by 10%.

\[
\text{New price after the first year} = 5 \times \left(1 + \frac{10}{100}\right) = 5 \times 1.1 = 5.5 \text{ dollars}
\]

### Step 2: Determine the cost of 1 kg of cheese at the end of the second year
The price increases again by 10% in the second year.

\[
\text{New price after the second year} = 5.5 \times \left(1 + \frac{10}{100}\right) = 5.5 \times 1.1 = 6.05 \text{ dollars}
\]

### Step 3: Calculate the amount of cheese that can be bought for $10
We now know that at the end of the second year, 1 kg of cheese costs $6.05. We need to find out how many grams of cheese can be bought for $10.

First, find the amount of cheese that $10 would buy in kilograms:

\[
\text{Amount in kg} = \frac{10}{6.05} \approx 1.65 \text{ kg}
\]

### Step 4: Convert kilograms to grams
Since there are 1000 grams in a kilogram, convert the amount to grams:

\[
\text{Amount in grams} = 1.65 \times 1000 \approx 1650 \text{ grams}
\]

### Final Answer:
At the end of the second year, you could buy approximately **1650 grams** of cheese for $10.

Would you like to dive into more details or have any questions?

Here are 5 related questions:
1. What would be the price of 1 kg of cheese after the third year if it continues to rise by 10% each year?
2. How would the amount of cheese bought for $10 change if the price increase was 15% each year instead?
3. What would be the price of 500 grams of cheese at the end of the second year?
4. How much would 2 kg of cheese cost at the end of the second year?
5. If you had $20

Learn how to calculate the amount of cheese that can be bought for $10 after two consecutive years of 10% price increases. This problem involves calculating percentage increases, unit conversions, and practical application of mathematical concepts in economics. Suitable for students in Grades 7-9.

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