Another lengthy concept D: I didn't post yesterday so I thought I'd post a difficult-to-understand-concept today. (: New blogskin, by MMJ. So here it goes, with a simple example :D

In the similtaneuous world, we always have to make equations (also known as number statements) to make solving easier. We need to at least have 2 of these equations to solve the question. However, make as many equations as you can I choose out the 2 most simplest ones. Look at the below equations I formed from the question:

1. 5/5 [P] + 3/3 [B] -> 80

2. 3/5 [P] + 1/3 [B] -> 36

3. 2/5 [P] + 2/3 [B] -> 44

Lemme explain how all the above equations are formed. For [1], it is mentioned that 80 pears and bananas at first. So, all of the pears and bananas make up to 80. For [2], it is mentioned that when 2/5 of the pears and 2/3 of the bananas were eaten, there were 36 of these fruits left. So, it is obvious that 3/5 of the pears and 1/3 of the bananas make up to 36. 3/5 of the pears and 1/3 of the bananas refers to the amount of fruits that were left. For [3], when we take the total[80] minus away the number of fruits left[36], we can find the number of fruits that were taken away[44]. Thus, 44 is equivalant to 2/5 of the pears and 2/3 of the bananas.

Next, we choose which 2 equations to choose. I choose [1] and [2]. Any of the above 2 equations is acceptable. Keep this in mind - What is the question asking for? How many pears were there in the basket at first? They are looking for pears, not bananas. Thus, we have to make the OTHER object, which is the banana, THE SAME. Continue reading to see what I mean.

5/5 [P] + 3/3 [B] -> 80

3/5 [P] + 1/3 [B] -> 36

Look at the 2nd equation. There are 1/3[B]. So, we make the bananas in the first and second equation the same. Thus, I multiply the 2nd equation numbers [3/5], [1/3] and [36] by 3, to get my third equation. (The one in bold)

The purpose of making the other object the same is to totally cancel it. What I mean is...

9/5 [P] + 3/3 [B] -> 108

5/5 [P] + 3/3 [B] -> 80

How do I know these? Simple - Since we used the second equation to make the same as the first one, we take the first one to compare. Notice that they have a similar item - 3/3 [B]. Then, when we minus, we will cancel out all the stuff that are same. Look..

9/5 [P] + 3/3 [B] -> 108

5/5 [P] + 3/3 [B] -> 80

We minus them together...

9/5 [P] + 3/3 [B] -> 108
5/5 [P] + 3/3 [B] -> 80

9/5 [P] - 5/5 [P] -> 108 -80

4/5 [P] -> 28

Since we know that 4/5 [P] is 28, we find 5/5 [P].

4/5 [P] -> 28

1/5 [P] -> 28 / 4 = 7