Math Problem Solving Strategies Part-1

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Here are some simple examples, where by doing guesswork one can score well.

Example 1

Q. The sum of 2 consecutive odd numbers is 44. Find the two integers.

Answer:

Sum: refers to adding numbers

Consecutive: Odd number and the next odd number that immediately follows the first one

Guessing implies picking any two numbers, adding them, and checking if it is equal to 44

. Here 32 is smaller than 44, go for big numbers.

Much closer

. Correct!

Example 2

Q. Tickets cost 5 dollars for children and 12 dollars for adults for a play. Number of tickets sold amount to 163 dollars. How many teachers and children went to the play?

Answer:

Doing guess work:

Let’s assume 3 children tickets were sold, then, 17 adult tickets were sold

The total is too high.

So, let’s go the other way round, assume 14 children tickets were sold & 6 adult tickets were sold

The total is a little too low.

Go, somewhat less for child and we have 12 children & 8 adult tickets sold

Finally we work much closer with 11 tickets for children and 9 tickets for adults and we get:

The correct Answer.

Example 3

Q. Modifying Example # 2. Tickets cost 5 dollars for children and 12 dollars for adults. A total of 20 people could go to the play. There must be at least 2 teachers to supervise the children, but no more than 10. Find all possible ways & how can school minimize the cost?

This problem involves making a list

If 2 teachers go, then 18 children will go

If 3 teachers go, then, 17 children will go

and so forth...

As you can see, the less teacher they send, the less the cost.

The least expensive case is to send 2 teachers and 18 children.

Try to follow logic for calculation and not merely work around extensive and elaborate calculations which will not fetch you an answer for minutes of hard work.