Maths-
General
Easy

Question

A group of friends decided to divide the straight $ 20 cost of a trip equally among themselves. When two of the friends decided not to go on the trip, those remaining still divided the straight $ 800 cost equally, but each friend's share of the cost increased by. straight $ 20 How many friends were in the group originally?

hintHint:

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 straight $ 800 equally, two of them decided to not go on the trip, then the remaining friend’s share of the cost increases by straight $ 20  
    • 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 straight $ 800 over x..
    Now, when two friends decided not to go on trip
    Then,
    Contribution of each friend become
    S fraction numerator 800 over denominator x minus 2 end fraction
    Step 2 of 2:
    According to question, the new cost per friend increased by straight $ 20.
    So,
    fraction numerator 800 over denominator x minus 2 end fraction minus 800 over x equals 20
    Now we have to solve this above equation.
    So,
    800 open parentheses fraction numerator 1 over denominator x minus 2 end fraction minus 1 over x close parentheses equals 20
    open parentheses fraction numerator 1 over denominator x minus 2 end fraction minus 1 over x close parentheses equals 1 over 40
    fraction numerator x minus left parenthesis x minus 2 right parenthesis over denominator x left parenthesis x minus 2 right parenthesis end fraction equals 1 over 40
    fraction numerator 2 over denominator x left parenthesis x minus 2 right parenthesis end fraction equals 1 over 40
    On further calculation,
    x left parenthesis x minus 2 right parenthesis equals 80
    x squared minus 2 x minus 80 equals 0
    Step 3 of 3:
    Using factorisation method, we solve above quadratic equation
    So,
    x squared minus 10 x plus 8 x minus 80 equals 0
    x left parenthesis x minus 10 right parenthesis plus 8 left parenthesis x minus 10 right parenthesis equals 0
    left parenthesis x plus 8 right parenthesis left parenthesis x minus 10 right parenthesis equals 0
    So, the solutions will be
    x = -8
    x = 10
    Since, The number friends can not be negative.
    So, x space equals space minus 8 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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