I think this one is C - both combined are sufficient.
We are dealing with 2 unknown variables (number of people (n), and the admission fee (f)). Note the total revenue generated will be T = n*f.
(1) gives us T = nf = (n+100)(f-0.75). Expanding the right side, we get
nf = nf -0.75n + 100f - 75
0.75n = 100f -75
This is an equation with 2 unknowns, which we can't solve for n.
(2) is similar. It gives us T = nf = (n-100)(f+1.50). Expanding gives us
nf = nf +1.50n -100f -150
-1.50n = -100f - 150
Again this is an equation with 2 unknowns.
However, if we combine (1) and (2), we get 2 linear equations for the 2 unknowns, so we should be able to solve for each variable. Adding the equation from (2) to the equation from (1) gives us
(0.75n = 100f - 75)
+(-1.50n = -100f -150)
= -0.75n = -225
This we can solve for n=300. Then, plugging n=300 back into one of the original equations gives us f=3.
We are dealing with 2 unknown variables (number of people (n), and the admission fee (f)). Note the total revenue generated will be T = n*f.
(1) gives us T = nf = (n+100)(f-0.75). Expanding the right side, we get
nf = nf -0.75n + 100f - 75
0.75n = 100f -75
This is an equation with 2 unknowns, which we can't solve for n.
(2) is similar. It gives us T = nf = (n-100)(f+1.50). Expanding gives us
nf = nf +1.50n -100f -150
-1.50n = -100f - 150
Again this is an equation with 2 unknowns.
However, if we combine (1) and (2), we get 2 linear equations for the 2 unknowns, so we should be able to solve for each variable. Adding the equation from (2) to the equation from (1) gives us
(0.75n = 100f - 75)
+(-1.50n = -100f -150)
= -0.75n = -225
This we can solve for n=300. Then, plugging n=300 back into one of the original equations gives us f=3.
