PSLE
Julian packed 406 muffins into large and small boxes. He filled each large box with 18 muffins and each small box with 8 muffins. All the boxes were full and no muffins were left over. What was the least number of boxes used by Julian?
To have the least number of boxes, Julian had to use as many as large boxes as possible.

If Julian used only large boxes,
number of large boxes used
= 406 ÷ 18
= 22 r 10 (x) There should be no remaining muffins left.

If 22 large boxes are used, there are 10 muffins left, Julian had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Julian used 21 large boxes,
number of muffins to be packed in small boxes
= 406 - (21 x 18)
= 406 - 378
= 28

Number of small boxes needed to pack 28 muffins
= 28 ÷ 8
= 3 r 4 (x)

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

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

Number of small boxes to pack 46 muffins
= 46 ÷ 8
= 5 r 6 (x)

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

If Julian used 19 large boxes,
number of muffins to be packed in small boxes
= 406 - (19 x 18)
= 406 - 342
= 64

Number of small boxes to pack 64 muffins
= 64 ÷ 8
= 8 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Julian used
= 19 + 8
= 27

Answer(s): 27