PSLE
Nick packed 416 muffins into large and small boxes. He filled each large box with 10 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 Nick?
To have the least number of boxes, Nick had to use as many as large boxes as possible.

If Nick used only large boxes,
number of large boxes used
= 416 ÷ 10
= 41 r 6 (x) There should be no remaining muffins left.

If 41 large boxes are used, there are 6 muffins left, Nick had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Nick used 40 large boxes,
number of muffins to be packed in small boxes
= 416 - (40 x 10)
= 416 - 400
= 16

Number of small boxes needed to pack 16 muffins
= 16 ÷ 6
= 2 r 4 (x)

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

If Nick used 39 large boxes,
number of muffins to be packed in small boxes
= 416 - (39 x 10)
= 416 - 390
= 26

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

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

If Nick used 38 large boxes,
number of muffins to be packed in small boxes
= 416 - (38 x 10)
= 416 - 380
= 36

Number of small boxes to pack 36 muffins
= 36 ÷ 6
= 6 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Nick used
= 38 + 6
= 44

Answer(s): 44