Problem Solving

A recipe for soda requires W liters of water for every liter of syrup. If soda is made according to this recipe using M liters of syrup, and sold for J dollars per liter, what will the be gross profit, in dollars, if syrup costs K dollars per liter and water costs nothing?

1. m(w+j-k)
2. jm(1/w+1)
3. m(jw-k)
4. (j-k)m
5. jm(1+w)-km

HELP!

This is a question from MGMAT, and pretty much straight forward. It would be better if you tell us "what did you not understand from the official explanation"

Oh I got this question from a Kaplan practice test, they didn't give me an official explanation. I realize it's asking for gross profit, but I guess I have no idea how to start solving a question like this.

Thanks.

A recipe for soda requires W liters of water for every liter of syrup. If soda is made according to this recipe using M liters of syrup, and sold for J dollars per liter, what will the be gross profit, in dollars, if syrup costs K dollars per liter and water costs nothing?

We have to find the profit (no difference between profit and gross profit here). The formula for profit is:
Profit = Selling Price - Cost Price
or P = SP - CP

Now we have to find out CP and SP
Cost price
1 liter of syrup costs K dollars
M liters of syrup cost M*K dollar.
Water is free.
So the cost price for soda is M*K dollars
And we will have M*(1+W) liters of soda

Selling Price
Amount of soda = M*(1+W)
Selling price of 1 liter of soda is J
Selling price of M*(1+W) liters of soda is J*M*(1+W)

Profit = J*M*(1+W) - M*K
now you can simplify the equation

Answer:
3. m(jw-k)


For 1 ltr of syrup you need W lts of water.

=> soda made is : M * W ltrs

each ltr of soda is sold at K dollars

Total Number of Dollars to sell soda = M * W * J

Total Dollars to make the soda = M * K (Since water is Free)

profit = Sell Price - Cost Proce

= M*W*J - M * K
= M(J*W - K)

which is the right answer??????????????

kishore wrote:Answer:
=> soda made is : M * W ltrs

This is the standard pitfall for GMAT.
You have to mix 1 liter of syrup with W liters of water, so the quantity of resulting solution/soda is 1 + W not W liters...

Sorry I dropped the ball on that.

the answer is E

You can solve this problem by choosing numbers for the variables and then testing each answer choice. You are much better at arithmetic than at algebra, remember that.

w = 2; m = 3; j = 4; k = 5

You'll end up with a profit of 21. Just plug in the numbers and see that the answer is E. Took me about 2 minutes.

Why do we have (1+W)? I can follow the rest...I'm just not sure why the 1 is added in.

dalwow,

The problem tells you that you need W liters of water for every liter of syrup. How many liters of water do you need for M liters? Well, if you need 2 liters of water for every liter of syrup, then how many do you need for, say, 3... the answer is 2 x 3 = 6

Similarly, in the problem, your total mix will be:

M (liters of syrup) + MW (total liters of water)

You then multiply this total by J dollars, which gives you the revenue.

Then, you get your cost which is MK (total liters of syrup multiplied by the cost K)

You then calculate your profit:

J(M + MW) - MK

or

JM(1 + W) - MK

Hope this makes things clear for you.

The algebraic solution is certainly elegant, but, on the exam, I would still use the arithmetic approach.

Even i used arithemetic.. it makes lot more sense, less confusing and saves time .

AleksandrM-

Thanks. That's the explanation I needed, it's just because the M was factored out. I appreciate you taking time to explain that.