This brief article investigates the line of thinking that may be used in solving a particular problem.

The reasoning applied is not unlike a computer programmer's, i.e a programmer thinks in terms of variables and groups (classes).

There are 60 people. Some eat 3 meals a day and some eat 4 meals a day. In one particular day, 213 meals are consumed by those 60 people. How many ate 4 meals?

First step: Eliminate all information not relevant to the problem.

The original question had more detail, but I already discarded those ...

Second step: Determine all entities that have quantities attached to them.

• people
• meals
• days

Third step: Are any of those entities grouped?

Yes, people are divided into two groups, those ones that eat 3 meals a day, and those that eat 4 meals a day. So now we have:

• people that eat 3 meals a day
• people that eat 4 meals a day
• meals
• days

Fourth step: Determine which of these entities are unknown.

The number of people of each group are unknown. This makes them variables. We allocate them the letters x and y. Note that the other 2 entities' quantities are known:

• people that eat 3 times a day = x
• people that eat 4 times a day = y
• meals = 213
• days = 1

Fifth step: Form as many equations as needed using these variables.

Since there are 2 unknowns, we need 2 equations:

1. There are 60 people:
   x + y = 60 (1)
2. The x people eating 3 meals that day + The y people eating 4 meals makes 213 meals that day in total:
   3x + 4y = 213 (2)

Sixth step: Solve these equations, derive the answer and confirm your results.

We can solve these two equations in the usual way. That is, substitute one in the other: