My son is entering Primary 3 next year and we will soon be introduced to those Arithmetic questions that require a bit of thinking to get the answer. The challenge is you can't use Algebra to answer the question.

Below is the introduction to such a question.

Amanda and Mary had 28 stickers altogether.
Amanda had 10 stickers more than Marry
How many stickers did Mary have?


Block diagram












Initially my approach was this and found it was wrong. I took 28/2-10=8 (Mary having 8 stickers) thinking that if you took the total and divide by 2, both will get the same amount. Since one got 10 more, the other would have gotten 10 less.

However, you don't get the right answer when you check. If Mary had 8 stickers, this means Amanda would have gotten 18 stickers. So 8+18=26 which is the wrong answer.

I tried an alternative approach which I read somewhere that you subtract the total with the difference and divide it by 2. 

Arithmetic 
Step 1: 28-10=18
Step 2: 18/2=9

So Mary had 9 stickers. If you check the answer, Amanda would have 19 stickers and their total stickers would be 28. 

I tried to convince myself with the working and answer with algebra and it made sense.

Alegebra
Let X be the number of stickers Mary had.
So Amanda had (X+10 stickers).

Step 1: X+(X+10)=28 is the total number of stickers.
Step 2: 2X+10=28
Step 3: 2X=28-10=18
Step 4: X=18/2=9
Mary had 9 stickers. 

As you can see, Arithmetic Step 1 & 2 is equivalent to Algebra Step 3 & 4. As such my 2nd approach is the right and I am now convinced why you deduct the "Differences" from the total and then divide it by 2. 

I expect future questions to  be tougher and I do hope to share with you. 




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