I think part of the point of this brochure is to think about the problems intuitively in the context they are presented. So in the first problem it's just kids trying to buy their first book, it would be silly to think Masha had a fraction of a kopeck (assuming you understand what a kopeck is, I really think it should have been translated as cent) and that the answer could be in range [7, 8). This may be what he talks about when he says that many academics fail at these problems.

Similarly, in problem #2 the cork indeed costs 0.5 kopecks but in this case we're just thinking about cost conceptually, not in terms of how much money a person actually has on hand.

Indeed, but it likewise seems intuitively reasonable to think that a book costs much more than 7 cents (or 7 times whatever the atomic unit of currency is) and that over 100 times the atomic unit is more reasonable.

Before 1917, they were divisible into 4 polushkas.

They're not. It's like a penny. Sure you may have parts of cents like with gas, but for girls buying books, it's the lowest currency value.

Long ago, many currencies had more divisions than they do now.

The penny of GBP came in quarter pennies (farthings) until 1950.

Half US-cent coins were made until 1857.

> (Problem #2 requires kopecks to be divisible.)

Does it? Did I fail at problem 2? I got:

Bottle + cork = 10

Bottle = 9cork

bottle/9 = cork

9(bottle + bottle/9) = 9(10)

9 bottle + bottle = 90

10 bottle = 90

bottle = 9

9 = 9cork

1 = cork

I read the second statement ("the bottle itself is 9 kopecks more expensive than the cork.") as:

Bottle = 9 + Cork

Your statement (Bottle = 9 * Cork) would be "the bottle is 9 times as expensive as the cork".

I solve it to:

Bottle = 9.5 Kopecks.

Cork = 0.5 Kopecks.

Works even if Kopecks are divisible: say the books value is 7.5, Mash must have 0.5 (7.5 - 7) and Misha 6.5 (7.5 - 1), however now when you combine them they sum to exactly 7.5 not less than, the only way to arrive at less than is if Masha has 0. So its always exactly 7

6.5 + 0.5 is 7.0, not 7.5, so that should be valid.

The book's cost can lie anywhere between [7, 8).

Right on the original typo, but still not convinced, I’ve rephrased to original to try to be clearer

> say the books value is 7.5, Mash must have 1.5 (7.5 - 7) and Misha 6.5 (7.5 - 1), however now when you combine them they sum to exactly 7.5 not less than

There are several problems with this:

- 7.5 - 7 is 0.5, not 1.5

- 1.5 + 6.5 is 8, not 7.5

- 0.5 + 6.5 is still less than 7.5

The problem specifies that 2x - 8 < x. There is no way to constrain this to the specific solution x = 7. Everything would work fine if the book cost -2.6 kopecks.

Thank you :) I’m being very clueless today

6.5 plus 0.5 is 7.0, they don't add up to exactly 7.5.

A kopeck is like a cent (1/100th of a ruble).