### Brain Teasers

# Coffee Grind

Math
Math brain teasers require computations to solve.

Fred had just started work in Hotel Plush and was dealing with a demanding but important guest. "Pour my coffee, boy! I want exactly 200ml coffee to which you will add enough full cream milk to make it 20% milk. Do it correctly and you may go about your other duties, get it wrong and I will call the manager," screeched the darling lady.

It was all Fred could do to stop his hands from trembling as he started to pour the coffee. He poured 200ml into the measuring jug, (he keeps one about his person at all times for such eventualities), then started to think about the milk. 20% of 200ml is 40ml but if he poured 40ml in, the volume would be 240ml, so it wouldn't be 20% milk any more. How much milk should he add?

It was all Fred could do to stop his hands from trembling as he started to pour the coffee. He poured 200ml into the measuring jug, (he keeps one about his person at all times for such eventualities), then started to think about the milk. 20% of 200ml is 40ml but if he poured 40ml in, the volume would be 240ml, so it wouldn't be 20% milk any more. How much milk should he add?

### Answer

The only volume we know is for the coffee, 200ml, so that's the starting point. We also know the final coffee is to be 20% milk, but that also means it is 80% coffee , so 80% = 200ml. That also means 20% = 50ml (80%/4=200ml/4), so he needs to add 50ml milk. Whether he puts anything else in there as well is between Fred and his conscience.Hide Answer Show Answer

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## Comments

m first and i have to say that it is a great one good job

I thought this was dead easy on the first reading but ended up getting it completely wrong A very clever teaser, well done.

The only thing that had me interested is "full cream milk." For two seconds, I wondered if that was a non-USA term for the product an intrusive USDA calls "whole milk." I thought maybe we would be excluding the regulation three point something percent fat from the 20%.

I solved it a bit differently, but it comes out the same in the end.

Let x be the amount of milk to add.

Therefore

x/(200 + x) = .2

Cross multiply to get

.2 * (200 + x) = x

Simplify

40 + .2x = x

40 = .8x

40/.8 = x

50 = x

Let x be the amount of milk to add.

Therefore

x/(200 + x) = .2

Cross multiply to get

.2 * (200 + x) = x

Simplify

40 + .2x = x

40 = .8x

40/.8 = x

50 = x

Worked it slightly differently: 20% is 1/5 (1 part out of 5), so the coffee is 80% of the whole, or 4 parts out of five. Just divided 200 ml. by 4 & got 50 ml. Nothing fancy. Very enjoyable teaser!

From what I read from the message given is the amount of coffee in the cup. It doesn't say a word about NOT adding an extra amount for cream or extras. Superb teaser! Keep it up

I thought it through a bit differently too... but I always tend to complicate things

Let f be the final volume.

Let m be the amount of milk.

200 + m = f

20% of f = m --> 0.2f = m

so f = m/0.2 = 5m

200 + m = 5m

200 = 4m

m = 50

Let f be the final volume.

Let m be the amount of milk.

200 + m = f

20% of f = m --> 0.2f = m

so f = m/0.2 = 5m

200 + m = 5m

200 = 4m

m = 50

but what I really wanted to say was... HAHAHAHA about whatever else he was gonna add to this nasty lady's coffee! "between him and his conscience", HAHAHAHAHAHA!!

Oh please. You want 4/5 to be coffee, so the total volume is 5/4 of 200 = 250. Any other approach is a waste of brain power.

Hence the answer. Sorry for using percentages instead of fractions if that's too confusing, however this approach is more flexible for more complicated calculations.

I think this is a great teaser, I did not get the right answer, because I suck at math.

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