Ans would be C.

Combining 2 statements we have : 100x-.75y=75
and 1.5y-100x=150

y can be calculated.

Hera x is the price and y is member.

amitansu wrote:Ans would be C.

Combining 2 statements we have : 100x-.75y=75
and 1.5y-100x=150

y can be calculated.

Hera x is the price and y is member.

Where did you get =75 and =150 from...?

Can someone please put a little light into this prob.??

Thanks.

x is fees amunt and y is no. of people assumed here.

so from 1: (x-0.75)(y+100)=xy

from 2: (x+1.5)(y-100)=xy

combining we can get y value.

Just to add to amitansu's comments:

First analyse the Question stem, and translate the english to algebra (assign variables):
Let the number of people = p
Let the admission fee = f
So from this we know that the total amount received in admission fees = (f)*(p)

Question is asking to get a value for p.

Now lets look at the first statement:
"if the admission fee had been $0.75 less" can be written as: f - 0.75
"100 more people had attended " can be written as: p + 100
We know that the club would have received (f)(p) in terms of admission fees, from the question stem.
so we can write out the following:
(f - 0.75)(p + 100) = fp

We need to find p ... can we do it ? no we cant ... because we have 2 unknowns and only 1 equation ! This is the golden rule, and you can quickly determine whether you have enough information to solve.
So (1) is INSUFF

Now lets look at the second statement:
"if the admission fee had been $1.50 more" can be written as: f + 1.50
"100 fewer people had attended " can be written as: p - 100
so we can write out the following:
(f + 1.50)(p - 100) = fp
Again ... as in statement 1, we have 2 unknowns and 1 equation. So INSUFF.

Now lets look at both statements together.
From (1) we know: (f - 0.75)(p + 100) = fp
From (2) we know: (f + 1.50)(p - 100) = fp

Now we have the 2 distinct equations that we need to solve for p.

Note: The 75 and the 150 values are gained by simplifying the equations (multiply out). See below.
(1) (f - 0.75)(p + 100) = fp can be simplified to 100f - 0.75x = 75
(2) (f + 1.50)(p - 100) = fp can be simplified to 1.5x - 100f = 150

Great Explanation! I couldn't figure out the equation before. thanks.

bigfernhead wrote:Great Explanation! I couldn't figure out the equation before. thanks.

Glad you found it useful.