Answer:
Okay, so I guess they also want to figure out the set up charge also- this is going to be a 2 variable equation.
X is the fee per person, and y is the set up charge.
25x+ y= 525
75x + y= 1475
So what you need to do is pick an equation, then isolate x:
25x + y= 525
25x= 525 -y
x= (525 - y)/25
Then, plug this in for x in the other equation:
75x + y= 1475 (original problem)
75((525 - y)/25) +y =1475 (subbed in x from other equation)
(75*525 -75y)/25 +y=1475 (distributed 75) (also could be multiplying fractions; 75/1)
(39375- 75y)/25 +y = 1475 (next I am simplifying the fraction)
1575 -3y +y = 1475 (Subtracting 1575; combining y's)
-2y = -100 (divide both sides by -2)
y=50
Okay, so now we know what the set up charge is- let's plug it into the unaltered first equation. (Note: At this point, you could really sub it into either equation and solve for x.)
25x+ y= 525
25x + 50 = 525
25x= 475
x= 19
Let's double check by subbing in y to the other equation as well:
75x + y= 1475
75x +50= 1475
75x= 1425
x= 19
Yay! It checks out in both problems!
Hope this helps, make sure to get a good night's sleep still.
