Question 214725
Let


x=cost per person (for 40 people) in dollars
y=total cost in dollars



If 40 people attend, then the cost per person 'x' is simply the total cost 'y' divided by the number of people going (40). In other words, {{{x=y/40}}} (eg: if the total cost is $80, then the cost per person is {{{80/40=2}}} dollars). This is your first equation.



Now if 36 people attend instead of 40, the cost per person will increase by $12. So this means that the new cost per person is {{{x+12}}} if 36 people go. This is equal to {{{y/36}}} (since the total cost is now divided among 36 people). So {{{x+12=y/36}}}. This is the second equation.



{{{x+12=y/36}}} Start with the second equation.



{{{y/40+12=y/36}}} Plug in {{{x=y/40}}}



{{{360(y/cross(40))+360(12)=360(y/cross(36))}}} Multiply EVERY term by the LCD {{{360}}} to clear out the fractions.



{{{9y+4320=10y}}} Multiply and simplify.



{{{9y=10y-4320}}} Subtract {{{4320}}} from both sides.



{{{9y-10y=-4320}}} Subtract {{{10y}}} from both sides.



{{{-y=-4320}}} Combine like terms on the left side.



{{{y=(-4320)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=4320}}} Reduce.



Since 'y' is the total cost, this means that the total cost is $4,320



{{{x=y/40}}} Move back to the first equation.



{{{x=4320/40}}} Plug in {{{y=4320}}}



{{{x=108}}} Divide



Since 'x' is the cost per person when 40 people were going, this means that the cost per person for 40 people is $108.