Tea Blend: Price of Inferior Tea

Date: 6/24/96 at 7:20:39
From: Anonymous
Subject: Tea Blend: Price of Inferior Tea

6kg of inferior quality tea are mixed with 3kg of high quality tea
which costs $2.00 per kilogram more than the inferior tea. The total 
price of the mixture is $24.00. What is the price of the inferior tea?

I started with the formula : x + x+2 = 24 but could not go further.
                             -   ---
                             6    3

Can you let me know how to determine the correct formulae to use?
I don't have a problem with using algebra; the difficulty I am
experiencing is how to work out the formula required to solve
the problem.

Help!

Date: 6/24/96 at 8:17:40
From: Doctor Anthony
Subject: Re: Tea Blend: Price of Inferior Tea

Remember to define terms before you write down the equations.

I will let x = price per kg of the cheap tea

         x+2 = price per kg of expensive tea

Total cost will be 6x + 3(x+2) = 24

                   6x + 3x + 6 = 24

                         9x = 18

                          x = 2

So cheap tea is $2 per kg.  

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 6/26/96 at 10:38:8
From: Doctor Jerry
Subject: Re: Tea Blend: Price of Inferior Tea

If the total cost of the inferior tea is x dollars per kg, then the 
total cost of the quality tea is (x+2) dollars.  Then, 6 kg of the 
inferior tea will have value 6x dollars (this is kg times dollars per 
kg) and the 3 kg of quality tea has value 3(x+2) dollars.  Total value 
if 24 dollars.  So 6x+3(x+2)=24.  Solution is x=2 dollars.

In your equation, the units don't balance.  On the left, you have kg 
divided by kg.  On the right, just dollars.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/