Articles of word problem

Simple question with a paradox

“I have three boxes, each with two compartments. One has two gold bars One has two silver bars One has one gold bar and one silver bar” You choose a box at random, then open a compartment at random. If that bar is gold, what is the probability that the other bar in the box […]

Time-and-Work and Motorcycle Tyres

A problem about motorcycle tyres, related to Time-and-Work or rate-of-work methods. This is not a homework question, nor, as far as I know, a contest question. It is intended as a challenge for Year 10/11 or 15/16-year olds, but should require no knowledge of calculus. Readers will no doubt be familiar with the type of […]

How To Know in a Application Sequence/Series Problem Which Variable is $a_{0}$ or $a_{1}$?

How do you determine what value takes on $a_{0}$ or $a_{1}$ in order to use either the infinite sum formula or $a_{n}$ formula? For example, consider the following two problems: A certain culture initially contains 10,000 bacteria and increases by 20% every hour. (a) Find a formula for the number N(t) of bacteria present after […]

$(n-7)(n+7)=$ some perfect square

This put in the context of a age problem will be: the product of my age seven years ago and seven years later is some perfect square Since this is a age problem that perfect square has to be between 1 and 100. I’ve try every factor of number between 1 and 100 inclusive, and […]

V.I. Arnold says Russian students can't solve this problem, but American students can — why?

In a book of word problems by V.I Arnold, the following appears: The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle. American school students had been coping successfully with this problem for over a decade. But […]

When does the two cars meet

At 10:30 am car $A$ starts from point $A$ towards point $B$ at the speed of $65$ km/hr, at the same time another car left from point $B$ towards point $A$ at the speed of $70$ km/hr, the total distance between two points is $810$ km, at what time does these two cars meet ? […]

Is there another simpler method to solve this elementary school math problem?

I am teaching an elementary student. He has a homework as follows. There are 16 students who use either bicycles or tricycles. The total number of wheels is 38. Find the number of students using bicycles. I have 3 solutions as follows. Using a single variable. Let $x$ be the number of students in question. […]

Spivak Chapter 2, problems 27 (and 28)

To be honest, I have no idea how to even start this problem. I’m sorry I don’t have any work to show, but I’m just at a blank. Help? Chapter 2: Problem 27: University B, once boasted $17$ tenured professors of mathematics. Tradition prescribed that at their weekly luncheon meeting, faithfully attended by all $17$, […]

Dr Math and his family question. How to solve without trial and error?

Dr Math told his family to write 4 different integers from 1 to 9 on to the 4 ]