When do you use the guess and check method?
You should use the guess and check method when you do not know how to solve a problem.
The guess and check method includes:
- make a logical guess
- test your guess
- adjust your guess based on results of #2 until you are correct
There are 20 children in the kindergarten class. The children are a mix of 5 year olds and 6 year olds. The total age of the children equals 108 years. How many 5 year olds are there?
Guess & check method:
- Let's guess that there are 10 five year olds.
- If there are 10 five year olds, there must be 10 six year olds since there are 20 children in total. Their combined age is equal to (10 x 5) + (10 x 6), or 110 years.
- Since 110 years is greater than 108 (the correct answer), our initial guess was incorrect. To get closer to the correct answer, we need to guess a higher number of five year olds (since five years is less than six years).
- Let's now guess that there are 12 five year olds.
- If there are 12 five year olds, there must be eight six year olds since there are 20 children in total. Their combined age is equal to (12 x 5) + (8 x 6), or 108 years. Therefore, the correct answer is 12 five year olds.