Math - Guess and Check

Guess and check is a powerful tool in solving more difficult math problems (i.e. differential equations). 

One tool that we need to answer guess and check problems is the table. We need to be able to construct a table of our guesses to see if it is getting nearer the desired answer.

Here is an example of how to make good guesses and how to fill out a table:

Patrick collected leaves for a Science project. He was able to collect 45 long and short leaves. There are 9 more long leaves than short leaves. How many long leaves and short leaves was he able to collect?

What are the clues that you can use?

* There are two kinds of leaves, long and short.

* There are 9 more long leaves than short leaves.

* The total number of leaves is 45.

We will use these clues to complete this table. Because the total is a multiple of 5, it makes sense to make guesses that are multiples of 5 as well. 

Long leaves	Short Leaves	Long leaves + Short leaves	Long leaves - short leaves (should be 9)
35	10	45	35-10 = 25
30	15	45	30-15 = 15
25	20	45	25-20 = 5

 

Because the difference that we want is between 5 and 15, we know that the numbers we want are near these pairs: 30,15 and 25,20. Knowing that 9 is close to 5, we will start out next table with 26 and 19.

Long leaves	Short Leaves	Long leaves + Short leaves	Long leaves - short leaves (should be 9)
26	19	45	26-19 = 7
27	18	45	27-18 = 9

There we go. Now we know that there are 27 long leaves and 18 short leaves for Patrick's Science project.

Let’s try another problem.

A seamstress bought some pieces of red and gold ribbon from the store. Each piece of red ribbon is 9 meters long. Each gold ribbon is 8 meters long. She bought 11 pieces of ribbon. The sum of the ribbons’ length is 95 meters. How many pieces of red ribbon and gold ribbon did she buy?

What are the clues that you can use?

* There are two kinds of ribbons: red and gold.

* Each red ribbon is 9 meters long.

* Each gold ribbon is 8 meters long.

*The total pieces of ribbons is 11.

* The total length of the ribbons is 95 meters.

Red ribbon	Gold ribbon	Total number of pieces	Total length of red ribbons (x 9 meters)	Total length of gold ribbons (x 8 meters)	Combined length of ribbons (should be 95 meters)
10	1	11	10x9= 90	1x8= 8	90+8 = 98
9	2	11	9x9= 81	2x8= 16	81+16 = 97
8	3	11	8x9= 72	3x8= 24	72+24 = 96
7	4	11	7x9= 63	4x8= 32	63+32 = 95

So, we can say that there are 7 red ribbons and 4 gold ribbons.

I will post more problems for this topic soon.