Notice that for both cases, there are 3 pens and 3 diaries in common.

The only difference is that 2 more diaries are bought in the 1st case and 2 more pens are bought in the 2nd case.

1st case : 3 diaries + 3 pens + 2 diaries,
Short of $6

2nd case : 3 diaries + 3 pens + 2 pens,
$4 left.

If you want to switch to the 1st case from the 2nd case, you'll have to swap the 2 pens for 2 diaries.

But the $4 left is not enough to top up the difference in price. $6 more is needed.

$4 + $6 = $10

This tells you that 2 diaries cost $10 more than 2 pens, since we have to top up $10

1 pen cost $1.25

So 2 pens cost $1.25 x 2 = $2.50

Then, 2 diaries cost $2.50 + $10
= $12.50

1 diary = $12.50 ÷ 2 = $6.25

With $30,

$30 ÷ $6.25 = 4 R $5



She can buy a maximum of 4 diaries with $30

I remember this is a heuristic question and there is a standard way of solving but cannot recall.

This question is a combination of excess-shortage and comparing differences