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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?

Respuesta :

TomShelby

Answer:

They were 10 friend

Explanation:

We can construct the equation system as follows:

[tex]\left \{ {{\frac{800}{friends} = a} \atop {\frac{800}{friends - 2} = a + 20}} \right.[/tex]

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

[tex]\frac{800}{friends - 2} = \frac{800}{friends} + 20[/tex]

[tex]800 = (\frac{800}{friends} + 20) \times (friends - 2)[/tex]

[tex]800 = 800 - \frac{1600}{friends} + 20friends - 40[/tex]

[tex]40 = 20 friends - 1600friends[/tex]

[tex]friends(40 - 20 friends) +1,600 = 0[/tex]

[tex]-20f^{2} + 40f + 1,600 = 0[/tex]

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

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