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

Answer:

They were 10 friend

Explanation:

We can construct the equation system as follows:

$\left \{ {{\frac{800}{friends} = a} \atop {\frac{800}{friends - 2} = a + 20}} \right.$

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

$\frac{800}{friends - 2} = \frac{800}{friends} + 20$

$800 = (\frac{800}{friends} + 20) \times (friends - 2)$

$800 = 800 - \frac{1600}{friends} + 20friends - 40$

$40 = 20 friends - 1600friends$

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

$-20f^{2} + 40f + 1,600 = 0$

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