Pies and Tarts

I am  a parent of a student in the school you gave a seminar. I found a problem in an assessment book which was confusing. Can you please help me to find out a solution to that problem?

I do not understand the way the answer given in the assessment book.
A Parent in Singapore

The Problem

Students with good number sense will know that the number of tarts and pies have to be in certain multiples given that they do not come in halves and quarters in a shop.

The ratio 3 : 2 tells us that tarts are in multiples of 3 (and pies in multiples of two) but as the tarts are packed in boxes of 4's, it must be in a common multiple of 3 and 4 (12). In the same way, the pies come in common multiple of 2 and 3 (6).

The least possible number for this to happen is 36 tarts and 24 pies - 9 boxes of 4 tarts and 8 boxes of pies. These will be $9 x $5 and 8 x $4 or $45 + $32 = $77.

It is also given that if all the tarts and pies are sold then they will bring in $770.

I think you can finish this up now.

This problem is based on ratio (P5), multiples (P4) and some basic multiplication and division (P3) and addition (P1).

This is a challenging P5 or P6 problem.

Note: P5 = Grade 5

Skeleton of the Solution