Question

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

Answer 1

They were 10 friend

Step-by-step explanation:

We can construct the equation system as follows:

`\left \{ {{(800)/(friends) = a} \atop {(800)/(friends - 2) = a + 20}} \right.`

we can solve for the number of friend by using subtritution:

`(800)/(friends - 2) = (800)/(friends) + 20`

`800 = ((800)/(friends) + 20) * (friends - 2)`

`800 = 800 - (1600)/(friends) + 20friends - 40`

`40 = 20 friends - 1600friends`

`friends(40 - 20 friends) +1,600 = 0`

`-20f^(2) + 40f + 1,600 = 0`

we get a quadratic formula we solve for the positive root

f = 10

We know check if the root is correct:

800 / 10 = 80

800 / (10 - 2) = 100