Question

# A group of friends decided to divide the cost of a trip equally among themselves. When two of the friends decided not to go on the trip, those remaining still divided the cost equally, but each friend's share of the cost increased by. How many friends were in the group originally?

Hint:

**Hint:**

- Here we will first make an equation using the given condition and then solve it.

## The correct answer is: Number of friends were in the group originally is 10.

### Explanation:

- We have given a group of friends decided to divide equally, two of them decided to not go on the trip, then the remaining friend’s share of the cost increases by
- We have to find the number for people were in the group originally .

Step 1 of 2:

Let the number of friends were in the group originally be x.

Then, Contribution of each friend will be .

Now, when two friends decided not to go on trip

Then,

Contribution of each friend become

Step 2 of 2:

According to question, the new cost per friend increased by .

So,

Now we have to solve this above equation.

So,

On further calculation,

Step 3 of 3:

Using factorisation method, we solve above quadratic equation

So,

So, the solutions will be

x = -8

x = 10

Since, The number friends can not be negative.

So, Will be rejected.

Therefore, x = 10 is the correct answer.

Final answer:

Hence, Number of friends were in the group originally is 10.

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