PSLE
Owen packed 456 muffins into large and small boxes. He filled each large box with 14 muffins and each small box with 12 muffins. All the boxes were full and no muffins were left over. What was the least number of boxes used by Owen?
To have the least number of boxes, Owen had to use as many as large boxes as possible.

If Owen used only large boxes,
number of large boxes used
= 456 ÷ 14
= 32 r 8 (x) There should be no remaining muffins left.

If 32 large boxes are used, there are 8 muffins left, Owen had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Owen used 31 large boxes,
number of muffins to be packed in small boxes
= 456 - (31 x 14)
= 456 - 434
= 22

Number of small boxes needed to pack 22 muffins
= 22 ÷ 12
= 1 r 10 (x)

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

If Owen used 30 large boxes,
number of muffins to be packed in small boxes
= 456 - (30 x 14)
= 456 - 420
= 36

Number of small boxes to pack 36 muffins
= 36 ÷ 12
= 3 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Owen used
= 30 + 3
= 33

Answer(s): 33