Question

A group of people are having a dinner that costs $160, which is to be shared equally. If two more persons join the group and share the same cost, each will pay $4 less. Find the original number of people in the group.

Answer 1

8 people in the original group.

Explanation:

Let x be the number of people who were originally present for the dinner that cost $160. Their average cost per person would be:

$160/x

If 2 more people join, there are x+2 people. Ignoring the awkward situation that they apparently did not order any additional food, they agree to share the cost of the dinner. The average cost is now:

$160/(x+2)

We are told that this new average is now $4 less per person.

$160/(x+2) = ($160/x) - $4

$160 = (($160/x) - $4)(x+2)

x = 8 people