An example problem of **indirect proportion** (or inverse proportion) involves two quantities where one increases as the other decreases, such that their product remains constant. 

### Example Problem:
A construction crew is working on a project. It takes 12 workers 10 days to complete the job. How many days will it take if there are only 8 workers?

### Solution:
Let the number of workers be \( W \) and the number of days be \( D \).

In an indirect proportion, the product of the two quantities (workers and days) remains constant:

\[
W_1 \times D_1 = W_2 \times D_2
\]

Where:
- \( W_1 = 12 \) workers,
- \( D_1 = 10 \) days,
- \( W_2 = 8 \) workers,
- \( D_2 \) is the unknown number of days.

Now apply the inverse proportion formula:

\[
12 \times 10 = 8 \times D_2
\]

\[
120 = 8 \times D_2
\]

Solve for \( D_2 \):

\[
D_2 = \frac{120}{8} = 15 \text{ days}
\]

### Answer:
It will take 15 days for 8 workers to complete the same job.

Would you like further details or explanations?

---

### Related Questions:
1. What is the formula for indirect proportion?
2. Can you explain the difference between direct and indirect proportions?
3. If the number of workers increased to 16, how many days would they need to complete the job?
4. How can you apply indirect proportion in real-life scenarios?
5. What happens if both quantities in a proportion increase or decrease?

### Tip:
In inverse proportion problems, always check if the product of the two variables remains constant to confirm the relationship.

Explore how to solve an inverse proportion problem where 12 workers take 10 days to complete a job, and determine how long it will take 8 workers. This step-by-step solution covers the key concepts of indirect proportion, including the formula W1 × D1 = W2 × D2. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation