Tuesday, September 13, 2011

Math Beast Challenge problem

From MGRE's Math Beast Challenge page, we have the following problem:

This Week's Problem: "Candy Bar Sales"

Q: James bought c candy bars, each at a price of p dollars. He then sold s of those candy bars, each at a price of y dollars. If James made a profit of x dollars, which of the following represents the number of candy bars that James sold?


(A) (pc – x)/y

(B) (x – pc)/y

(C) xy – pc

(D) (x + pc)/y

(E) (pc – y)/x

This seems fairly straightforward. My answer will be in the comments. The official answer will be displayed next week.



Kevin Kim said...

We know the following:

c = # of candy bars James bought

p = price per (purchased) bar

s = # of bars sold by James

y = price per sold bar

x = James's profit after the buying and selling

The basic formula for profit is:

[$ from sales] - [$ spent]

Based on the above, "$ from sales" would be represented as


and "$ spent" would be represented as


So our formula looks like this:

x = sy - cp

The problem is asking for the number of candy bars sold, so we're solving for s, which we can do through the following steps:

x = sy - cp

x + cp = sy

(x + cp)/y = s

or, flipped:

s = (x + cp)/y

The answer is, in my opinion, D, which has been written as

(x + pc)/y.

(Quad erat demonstrandum, Mike!)

Charles said...

Yay! I arrived at the same answer you did in exactly the same way.

I'm pretty proud of myself, considering how much I've forgotten about math (I don't even remember what this type of math is called, or if it is even an official "type"). Unless it's in the form of a programming problem (I still program from time to time), I usually just freak out.

But yeah, this was pretty straightforward.

Horace Jeffery Hodges said...

I arrived at the same answer instantly by a wildly random guess, so I 'guess' my method is superior.

Jeffery Hodges

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