Answer:
10 friends
Step-by-step explanation:
Let the initial number be x friends so that when 2 decide not to go, the remaining will be x-2. The final cost per person minus initial cost per person is $20.
Initial cost per person was [tex]\frac {800}{x}[/tex]
Final cost per person is [tex]\frac {800}{(x-2)}[/tex]
[tex]\frac {800}{(x-2)}-\frac {800}{x}=20\\\frac {800x-800(x-2)}{x(x-2)}=20\\\frac {800x-800x+1600}{x^{2}-2x}=20\\ 1600=20(x^{2}-2x)\\80=x^{2}-2x\\x^{2}-2x-80=0\\(x+8)(x-10)=0[/tex]
x=-8 or 10
Therefore, the original number was 10 friends
