https://file.aiquickdraw.com/mathbot/file/17268601345875ael9xio.jpg

Let's break down the problem step by step:

- The total cost of eatables is ₹96.
- Initially, let the total number of friends be \( x \).
- The initial contribution per person is \( \frac{96}{x} \).
- However, 4 people did not turn up, so the number of people who actually went is \( x - 4 \).
- The new contribution per person is \( \frac{96}{x - 4} \).
- Each person now pays ₹4 extra, which gives us the equation:
  \[
  \frac{96}{x - 4} = \frac{96}{x} + 4
  \]

### Now, let's solve the equation:

\[
\frac{96}{x - 4} - \frac{96}{x} = 4
\]

First, find a common denominator for the left side:

\[
\frac{96(x) - 96(x - 4)}{x(x - 4)} = 4
\]

Simplifying the numerator:

\[
\frac{96x - 96x + 384}{x(x - 4)} = 4
\]
\[
\frac{384}{x(x - 4)} = 4
\]

Now, multiply both sides by \( x(x - 4) \):

\[
384 = 4x(x - 4)
\]

Divide both sides by 4:

\[
96 = x(x - 4)
\]

Expand the right side:

\[
96 = x^2 - 4x
\]

Rearrange it to form a quadratic equation:

\[
x^2 - 4x - 96 = 0
\]

Solve using the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-96)}}{2(1)}
\]
\[
x = \frac{4 \pm \sqrt{16 + 384}}{2}
\]
\[
x = \frac{4 \pm \sqrt{400}}{2}
\]
\[
x = \frac{4 \pm 20}{2}
\]

This gives two possible solutions:

\[
x = \frac{4 + 20}{2} = 12 \quad \text{or} \quad x = \frac{4 - 20}{2} = -8
\]

Since \( x \) must be positive, the total number of friends initially was \( x = 12 \).

Thus, **12 friends** were originally supposed to go on the picnic, but after 4 did not turn up, **8 friends** went on the picnic.

Would you like a detailed explanation of any part, or do you have further questions?

Here are 5 related questions you can try:
1. If 3 people didn’t turn up, how much more would each friend have to pay?
2. What if the total amount spent was ₹120 instead of ₹96?
3. How would the equation change if 5 people didn’t show up instead of 4?
4. What if the friends initially planned to spend ₹96, but the cost increased to ₹120 at the picnic?
5. What would the equation look like if 6 people dropped out instead of 4?

**Tip**: In problems like these, setting up an equation based on the changes (like an increase in cost per person) is a key strategy to solving them systematically!

A group of friends went on a picnic and planned to spend ₹96 on eatables. As four of them did not turn up, the remaining friends had to pay ₹4 each extra. How many went on the picnic?

Solve a real-life word problem involving cost sharing using quadratic equations. A group planned to spend ₹96, but 4 people didn't show up, so the rest had to pay ₹4 extra. Learn how to set up and solve this algebraic equation. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation