Question

A group of friends shared expenses for a trip which cost 40 dollars. If there were 3 more people in the group each would have paid 3 dollars less. How many people were there in the group and how much did each pay?

Answer 1

initial number of friend: x

\[(40 \div x-3) \times (x+3) = 40\]

Answer 2

How would i solve that?

Answer 3

9 = 120/x - 3x
9x + 3x^2 = 120

then use quadratic equation to solve this

Answer 4

Um whats a quadratic equation

Answer 5

x = 5

Answer 6

These are the steps that zscdragon would have followed:

lets call the total number of people originally in the group x.
then, if the total cost was $40, we know each person must have paid $\(\displaystyle\frac{40}{x}\)

we are then told that if there were 3 more people in the group (i.e. (x+3) people) then each person would have paid $3 less (i.e. each person would then have paid $\(\displaystyle\frac{40}{x}-3\)).
since the total cost is the same (i.e. $40), we can therefore say that:\[(x+3)(\frac{40}{x}-3)=40\]therefore:\[\frac{(x+3)(40-3x)}{x}=40\]then, multiplying both sides by x we get:\[(x+3)(40-3x)=40x\]which expands to:\[\cancel{40x}-3x^2+120-9x=\cancel{40x}\]therefore:\[-3x^2-9x+120=0\]multiplying both sides by -1 we get:\[3x^2+9x-120=0\]dividing through by 3 we get:\[x^2+3x-40=0\]which factorises to:\[(x-5)(x+8)\]therefore:\[x=5\text{ or }-8\]and since the number of people cannot be negative we get:\[x=5\]therefore there were 5 people in the original group and each one paid $\(\displaystyle\frac{40}{5}=?\)

Answer 7

Thanks for your guys help

Answer 8

yw :)