P6 Math: Mr. Tan tarts

Mr. Tan packed 508 tarts into large and small boxes to sell. He filled each large box with 20 tarts and each small box with 12 tarts. All the boxes were full and there was no left over. What was the least number of boxes used by Mr. Tan ?

Solution:

Since the problem asks for the least number of boxes, then Mr. Tan should use as many as large boxes to pack. 

Now assume all tarts are packed with large boxes.

508 / 20 = 25R8, there is reminder of 8 tarts --> 8 tarts will not fill a small box !

Try to reduce number of large boxes, one by one

Number of L boxes	Number of tarts inside L box	Extra tarts	Number of S boxes	Fit
25	500	8	1	No
24	480	28	2	No
23	460	48	4	Yes

Hence, we found the solution with 23 large boxes and 4 small boxes. The least amount of boxes is 23 + 4 = 27.

If we try to solve by assuming all tarts are packed in small boxes, the iteration process is quite tedious and may find few solutions (where tarts can fit in the boxes) but not the smallest number of boxes. For example, the whole tarts can fit in 39 small boxes and 2 large boxes, a total of 41 boxes !