The instructions on a -gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires grams of coffee beans. What is the greatest number of properly brewed large mugs of coffee that can be made from the coffee beans in that bag?
- A)
- B)
- C)
- D)
- E)
Answer
B
Key insight
Dividing 350 by 20 gives 17.5, and half a mug is not a properly brewed mug, so the count is the whole part, 17.
Solution
Every properly brewed mug uses exactly grams, so mugs use grams and the requirement is . Divide:
Seventeen mugs use grams and leave grams, which is not enough for an eighteenth mug brewed properly. Hence the greatest number is .
The answer is .
Why this works
The quotient answers "how many -gram portions fit", but only whole portions can be brewed, so the answer is the integer part. Any problem of the form "how many complete items can be made from a fixed supply" is a floor division: compute the quotient and then round down, never to the nearest integer.
The trap
Rounding 17.5 up to 18, which is choice (C).
Common mistakes
- Rounding 17.5 up to 18, which is choice (C).
- Treating the leftover grams as a usable half-mug and counting it; the problem asks only for mugs brewed to the stated instructions.
Techniques
Set up the equation/formula and compute; no special trick needed