a group of people...

Question

a group of people contribute equal amounts of money to get $24 gift for a friend. If two more people contribute and they all paid equal amounts, they would each pay $1 less. How many people were there originally?

a) 6

b) 7

c) 3

d) 4

Answer 1

n = original number

24/n = x

24/(n + 2) = x - 1

From the second equation,

x = 24/(n + 2) + 1

But this must equal the same x as in the first equation.

24/n = 24/(n + 2) + 1

Multiply both sides by n(n + 2).

24(n + 2) = 24n + n(n + 2)

24n + 48 = 24n + n² + 2n

n² + 2n - 48 = 0

(n + 8)(n - 6) = 0

n must be positive, so

n = 6

(Same answer as in Mona's solution, but a different approach.)

Answer 2

This is the type of question that you can either do plug in or create two equations.

I did plug. We had to have number that are integer factors of 24.

So I did the factors and looked at the answers.

6 and 8 when divided into 24 give us 4 and 3 and that satisfies the question.

Answer a. 6

add two getting 8 and the difference in sharing is $4 and $3 which is what the question is looking for.