# Help with a puzzle

• Dec 13th 2011, 03:38 AM
nicoT30
Help with a puzzle
Hi there! On wednesday I'm having a really important test at University and in the practice-book I found a puzzle I just can't solve, it goes like this:

In a coffee storea new coffee is being prepared. It contains: 10kg of a $20/kg coffee and some of$12/kg. How many Kilos of $12/kg coffeemust the mix contain so that charging it$18/kg they obtain 10% profit over the cost?

Sorry if it's grammatically wrong.

Thanx !
• Dec 13th 2011, 07:54 AM
Wilmer
Re: Help with a puzzle
Quote:

Originally Posted by nicoT30
In a coffee storea new coffee is being prepared. It contains: 10kg of a $20/kg coffee and some of$12/kg. How many Kilos of $12/kg coffeemust the mix contain so that charging it$18/kg they obtain 10% profit over the cost?

Quite unclear; "charging it" means charging the mixture or only the $12 coffee? Is the$20:$12 including the 10%, or will it be sold at$22:$13.20 ? Anyhow, leaving the "profit out": x = kg of$20 coffee
[20x + 12(10 - x)] / 10 = 18
Solve to get x = 7.5 kg

Do you know the answer? We can probably figure out the meaning from that.
• Dec 13th 2011, 08:46 AM
Soroban
Re: Help with a puzzle
Hello, nicoT30!

The information is incomplete . . .

Quote:

In a coffee store a new coffee is being prepared.
It contains: 10kg of a $20/kg coffee and some of$12/kg.

How many kilos of $12/kg coffee must the mix contain so that charging$18/kg they obtain 10% profit over the cost?

Ignoring profit, we can reason as follow . . .

We have 10 kg of Brand A at $20/kg. . . Its value is:. $10\cdot20 \,=\,200$ dollars. We add $x$ kg of Brand B at$12/kg.
. . Its value is:. $12x$ dollars.

The total value of the mixture is:. $200 + 12x$ dollars. .[1]

The mixture will be $x+10$ kg at $18/kg. . . Its value is:. $18(x+10)$ dollars. .[2] We just described the value of the mixture in two ways. There is our equation! , $\hdots\quad200 + 12x \:=\:18(x+10)$ Solve for $x\!:\;\;12x + 200 \:=\:18x + 180 \quad\Rightarrow\quad 6x \:=\:20$ . . Hence: . $x \:=\:\frac{10}{3}\:=\:3\tfrac{1}{3}\text{ kg of Brand B}$ To determine 10% profit, we must know . . the unit cost of Brand A and Brand B. And this was not provided. • Dec 13th 2011, 03:00 PM nicoT30 Re: Help with a puzzle Really interesting :p I've burnt my mind and couldn't do it. About the 10% I got to this.. Real price of Mix = X So..$18= X + 10/100 X
$18= 110/100 X$18 / (110/100) = X
\$16,36 = X

Sorry about the way I wrote the equation, I did not learn the other way yet, I have to read the tutorial. I hope you have at least enjoyed a bit this problem :p

Thanx for helping!