PSLE
Wesley packed 362 muffins into large and small boxes. He filled each large box with 10 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 Wesley?
To have the least number of boxes, Wesley had to use as many as large boxes as possible.

If Wesley used only large boxes,
number of large boxes used
= 362 ÷ 10
= 36 r 2 (x) There should be no remaining muffins left.

If 36 large boxes are used, there are 2 muffins left, Wesley had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Wesley used 35 large boxes,
number of muffins to be packed in small boxes
= 362 - (35 x 10)
= 362 - 350
= 12

Number of small boxes needed to pack 12 muffins
= 12 ÷ 8
= 1 r 4 (x)

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

If Wesley used 34 large boxes,
number of muffins to be packed in small boxes
= 362 - (34 x 10)
= 362 - 340
= 22

Number of small boxes to pack 22 muffins
= 22 ÷ 8
= 2 r 6 (x)

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

If Wesley used 33 large boxes,
number of muffins to be packed in small boxes
= 362 - (33 x 10)
= 362 - 330
= 32

Number of small boxes to pack 32 muffins
= 32 ÷ 8
= 4 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Wesley used
= 33 + 4
= 37

Answer(s): 37