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!

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...

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?

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...

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

So with this working, and showing him that the numbers work in both equations, you should be able to convince him...

Re: Old guys arguin over math from long ago

Awesome :)...He gets it now lol.. Thanks for your time :)