If the price of sugar increases by 20%, by what percentage should a household reduce its consumption of sugar so that the budget remains the same?

Let's break down the problem step-by-step:

- Let the original price of sugar be \( P \) and the original consumption be \( C \).
- The original total expenditure on sugar is \( P \times C \).

Now, after a 20% increase in the price of sugar:
- The new price of sugar becomes \( P \times 1.2 \).
- Let the new consumption of sugar be \( C_{\text{new}} \), which the household needs to adjust to maintain the same budget.

The new total expenditure should remain the same, so:
\[
P \times C = P \times 1.2 \times C_{\text{new}}
\]
Now, canceling \( P \) from both sides of the equation:
\[
C = 1.2 \times C_{\text{new}}
\]
To find \( C_{\text{new}} \), rearrange the equation:
\[
C_{\text{new}} = \frac{C}{1.2}
\]
Now, we calculate the percentage reduction in consumption. The reduction is given by:
\[
\text{Percentage reduction} = \frac{C - C_{\text{new}}}{C} \times 100
\]
Substitute \( C_{\text{new}} = \frac{C}{1.2} \):
\[
\text{Percentage reduction} = \frac{C - \frac{C}{1.2}}{C} \times 100
\]
\[
\text{Percentage reduction} = \left(1 - \frac{1}{1.2}\right) \times 100
\]
\[
\text{Percentage reduction} = \left(1 - 0.8333\right) \times 100
\]
\[
\text{Percentage reduction} = 0.1667 \times 100 = 16.67\%
\]

So, the household should reduce its sugar consumption by **16.67%** to maintain the same budget.

Would you like more details on any step? Here are some related questions you might find helpful:

1. How does a 10% price increase affect consumption under similar conditions?
2. What is the general formula for adjusting consumption after a price change?
3. How does elasticity of demand factor into this kind of problem?
4. What if the price increase was 30% instead of 20%? How would that change things?
5. How can we model such changes for a household with multiple goods in their budget?

**Tip**: When facing price changes, thinking in terms of relative percentages is a powerful tool for maintaining a fixed budget.

Learn how to calculate the percentage reduction in sugar consumption required to maintain the same budget after a 20% price increase. This detailed explanation covers key concepts like proportionality and budget constraints. Suitable for students in 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