Question

Mitchell is a big coffee fan, so he always takes care of coffee brewing at the office. Normally he uses 100100100 grams of Robusta coffee to prepare 101010 cups of coffee. His friend brings him a packet of Arabica coffee and tells him that he should use 20\%20%20, percent more than usual when brewing Arabica coffee. How many grams of coffee should he use to make a 15-cup pot of Arabica coffee?

Answer 1

Normally he uses 100,100,100 grams of coffee for 101,010 cups.

That's (100,100,100) / (101,010) = 990.992 grams per cup.

If he wants to use 20% more, that would be

(1.2) x (990.992) = 1,189.19 grams per cup.

To make a pot of 15 cups, he would need to use

(15) x (1.2) x (990.992) = 17,837.9 grams,

(about 39.3 pounds of coffee) .
___________________________________________

This troubles me. He normally uses almost 2.2 pounds of coffee
for every cup, and now he has to cram 39 pounds of coffee into
that little pot. It seems that Mitchell has a serious caffeine problem,
and plus he's spending a fortune on coffee. How can this be ?
These numbers just don't make sense !

Could it be that the numbers given in the question are not what they
seem to be ? Could it be that all those ones and zeros are not really
decimal numbers, i.e. written in base-ten ? Could it be that they are
actually binary numbers instead ? The question doesn't tell us what
base the numbers are written in ... but the results I got from my
calculations are just so totally weird ! I'll go through the whole thing
again, only this time, I'll assume that the numbers in the question are
binary numbers ... base-2 ... and see how that works out.

Normally he uses 100100100 grams of coffee. If that's a binary
number, then it translates into the decimal number 292 grams.
Ah hah !

He uses that to prepare 101010 cups. If that's a binary number,
then it translates into 42 cups.

This is looking much better. In fact, I think the coffee has suddenly
become pretty weak ! Lets carry on . . .

NOW, Mitchell normally uses 292 grams for 42 cups.

20% more than that is (1.2) x (292/42) grams per cup.

To make 15 cups of the new stuff, he'll need

(15) x (1.2) x (292/42) = 125.142 grams of coffee

about 4,4 ounces !

Much better !

I suppose 'Maimom61' expects the answer as a binary number.
I'll need to round the amount of coffee to the nearest whole
number first, because I don't remember how to write decimals
in binary.

125.142 grams, rounded to the nearest whole gram, is 125 grams.

As a binary number, that's 1 1 1 1 1 0 1 grams.

Answer 2

180 grams

Explanation:

Mitchell has to use more coffee than usual for two reasons: First, he's making a larger pot than usual (15(15 cups rather than 10)10). And second, he's using the Arabica coffee, which requires 20\%20% more coffee for the same strength.

Instead of brewing \blue{10}10 cups, Mitchell wants to brew \red{15}15 cups, which means he has to use \dfrac{\red{15}}{\blue{10}}=\purple{1.5}

10

15

​ =1.5 times more coffee.

As his friend said, Mitchell also has to use \pink{20\%}20% more coffee than usual, so he'll have to multiply the amount of coffee by \green{1.2}1.2, or \green{120\%}120%.

The total amount of coffee he has to use is 100100 grams \times× \purple{1.5} \times \green{1.2} = 1801.5×1.2=180 grams.