A group of friends decided to divide the $800

I’ll write the problem as an equation:

n=Number of friends

c=Individual cost per friend

800/n=c

800=(n-2)(c+20)

800=(n-2)([800/n]+20)

800=800+20n-1600/n-40

0=20n-1600/n-40

20n^2-40n-1600=0

20(n^2–2n-80)=0

20(n-10)(n+8)=0

n=10 or n=-8

So there were 10 friends, let’s verify:

800/n=c

800/10=80

800/(10–2)=c+20

800/8=100

100=c+20=80+20

So yeah, 10 friends

Other way

800/(n-2) – 800/n =20

Simplifying, n(n-2) = 80

if we let n = x+1, this becomes (x+1)(x-1) = x² – 1 =80

x² = 81, so x = 9. Originally 10 friends less 2 leaving 8.

Price goes from $80/person to $100 per person

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