Store A already has 104 more apples than Store B.


If Store B continues to sell 32 apples in its current situation, the difference in apples between Store A and Store B will just simply widen further.

(You can draw a model to visualise this!)


Note that Store A’s apples do not change at all (the “constant”).


New difference
= 104 + 32 (because of the “widening” effect)
= 136


———————————————


In the end, we know that the final ratio of apples in Store A to apples in Store B is 5 : 1, due to the “5 times” information.


The difference in units will be 5u - 1u = 4u, which is going to be the 136 apples I mentioned.


4 units = 136 apples
1 unit = 34 apples
5 units = 170 apples


So, Store A has 170 apples (which doesn’t change throughout the question).



———————————————


Check working:


Store A has 170 apples at first.
Store B has 170 - 104 = 66 apples at first.


Store A has 170 apples in the end.
Store B has 66 - 32 = 34 apples in the end.


Check that 170 is the same as 34 x 5, meaning that Store A indeed has five times as many apples as Store B.

It’s possible to start with the end ratio 5 : 1 as well before incorporating the 32 and 104 later on, but this approach will turn a little too algebraic for the P5 level, so I will not be going down this path for the working

If for P6, can you advise me in ratio method?

The final ratio for store A to store B is 5 : 1.

We will put this as 5u : 1u (basically, 5 units to 1 unit). The ratio idea ends pretty much here, although I will put one ratio later on.

Store B got to this stage by selling 32 apples. This didn’t happen initially, so store B initially had (1u + 32) apples.

Store A remained at 5u for the entire question, since no buying or selling of apples took place.

Initial ratio A : B would appear like 5u : (1u + 32), although this isn’t exactly much of a ratio in practice.

We know that Store A had 104 more apples than Store B, so if we add 104 apples to Store B’s count for apples, we get the number than Store A had.

1u + 32 + 104 = 5u
1u + 136 = 5u

Clearly 5u is greater than 1u by a total of 4u, so

136 = 4u
4u = 136 (basically, 4 units is 136 in value)
1u = 34
5u = 170

So, store A had 170 apples.

So, to address your question, the “before” and “after” is incorporated into my ratios as 5u : (1u + 32) for the “before” and 5u : 1u for the “after”.

As for where the “constant” and “change” come into play, it has nothing to do with the topic of ratios itself. Rather, it comes due to the happenings in the story. Store B’s selling of 32 apples indicate a “change” while non-mention of anything about Store A’s apples indicate a “constant”.

As for “part”, I believe that is basically another name for “unit.