# Old guys arguin over math from long ago

• Sep 9th 2011, 07:57 PM
CorySCline
Old guys arguin over math from long ago
So we have ave a math problem that we are arguing on. This started as an argument between two 40 year olds looking through kid's math books. Here is the problem:

If there is 26 times more caffeine in a normal cup of coffee than in decaf and the total between them is 121.5 Grams of caffiene, how much is in each cup?

While I have no clue how to solve it, I can verify answers (Thank god my old brain retains that :) ). My logic says that:
Decaf + Regular = 121.5
Decaf * 26 = Normal

He is trying to tell me that Decaf = 4.67 and Caffien = 116.82. Rounded of course.

I can tell this is wrong because while Decaf + Regular is true, Decaf * 26 is not.

How can I prove him wrong here?

:)

Thanks!
• Sep 9th 2011, 08:25 PM
Prove It
Re: Old guys arguin over math from long ago
Quote:

Originally Posted by CorySCline
So we have ave a math problem that we are arguing on. This started as an argument between two 40 year olds looking through kid's math books. Here is the problem:

If there is 26 times more caffeine in a normal cup of coffee than in decaf and the total between them is 121.5 Grams of caffiene, how much is in each cup?

While I have no clue how to solve it, I can verify answers (Thank god my old brain retains that :) ). My logic says that:
Decaf + Regular = 121.5
Decaf * 26 = Normal

He is trying to tell me that Decaf = 4.67 and Caffien = 116.82. Rounded of course.

I can tell this is wrong because while Decaf + Regular is true, Decaf * 26 is not.

How can I prove him wrong here?

:)

Thanks!

Maybe the fact that, like you said, Decaf x 26 is wrong...
• Sep 9th 2011, 08:32 PM
CorySCline
Re: Old guys arguin over math from long ago
Yes. However, he is dense. He does not understand my logic. How do i solve the problem properly to show him the correct answer?
• Sep 9th 2011, 08:52 PM
Prove It
Re: Old guys arguin over math from long ago
Quote:

Originally Posted by CorySCline
Yes. However, he is dense. He does not understand my logic. How do i solve the problem properly to show him the correct answer?

Assuming that you are using the words "normal" and "regular" for the same thing...

\displaystyle \begin{align*} d + r &= 121.5 \\ 26d &= r \\ \textrm{Substitute the second equation into the first} \\ d + 26d &= 121.5 \\ 27d &= 121.5 \\ d &= 4.5 \\ \textrm{Substitute this answer into the second equation} \\ 26\cdot 4.5 &= r \\ 117 &= r \end{align*}

So with this working, and showing him that the numbers work in both equations, you should be able to convince him...
• Sep 9th 2011, 09:00 PM
CorySCline
Re: Old guys arguin over math from long ago
Awesome :)...He gets it now lol.. Thanks for your time :)