Last Sunday a certain store sold copies of Newspaper A for $1.00 each and
copies of Newspaper B for $1.25 each, and the store sold no other newspapers
that day. If r percent of the store's revenues from newspaper sales was from
Newspaper A and if p percent of the newspapers that the store sold were
copies of newspaper A, which of the following expresses r in terms of p?
This one was actually very tough for me. I first read it as r is for Newspaper A and p is for Newspaper B...
I was getting really frustrated as you can imagine.
Even when I reread this, it was still tough to come across the answer.
Il break it down:
x and y are the number of papers sold for A and B respectively.
100x/(x+y)=p and 100x/(x+1.25y)=r
lets rework p.
100x=px+py ---> 100x=p(x+y) ---> 100x/p=x+y ---> 100x/p-x=y
Plug in y in the second equation for r.
100x/(x+1.25(100x/p-x) multiply by p (make p the commen denominator)---> 100x/(xp/p+(125x-1.25xp)/p)
100x/((125x-.25xp)/p) take out the x---> 100x/x((125-.25p)/p) ---> 100p/(125-.25p) ---> 100p/(500/4-p/4)
100p/((500-p)/4) ---> 400p/(500-p)
This was ridiculous!!!