PSLE
John packed 406 muffins into large and small boxes. He filled each large box with 20 muffins and each small box with 6 muffins. All the boxes were full and no muffins were left over. What was the least number of boxes used by John?
To have the least number of boxes, John had to use as many as large boxes as possible.

If John used only large boxes,
number of large boxes used
= 406 ÷ 20
= 20 r 6 (x) There should be no remaining muffins left.

If 20 large boxes are used, there are 6 muffins left, John had to use less large boxes so that the rest of the muffins were packed in small boxes.

If John used 19 large boxes,
number of muffins to be packed in small boxes
= 406 - (19 x 20)
= 406 - 380
= 26

Number of small boxes needed to pack 26 muffins
= 26 ÷ 6
= 4 r 2 (x)

There should be no remaining muffins left. So, John had to use less large boxes.

If John used 18 large boxes,
number of muffins to be packed in small boxes
= 406 - (18 x 20)
= 406 - 360
= 46

Number of small boxes to pack 46 muffins
= 46 ÷ 6
= 7 r 4 (x)

There should be no remaining muffins left. So, John had to use less large boxes.

If John used 17 large boxes,
number of muffins to be packed in small boxes
= 406 - (17 x 20)
= 406 - 340
= 66

Number of small boxes to pack 66 muffins
= 66 ÷ 6
= 11 r 0 (✓) There is no remaining muffins left.

Least number of boxes that John used
= 17 + 11
= 28

Answer(s): 28