PSLE
Peter packed 336 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 Peter?
To have the least number of boxes, Peter had to use as many as large boxes as possible.

If Peter used only large boxes,
number of large boxes used
= 336 ÷ 18
= 18 r 12 (x) There should be no remaining muffins left.

If 18 large boxes are used, there are 12 muffins left, Peter had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Peter used 17 large boxes,
number of muffins to be packed in small boxes
= 336 - (17 x 18)
= 336 - 306
= 30

Number of small boxes needed to pack 30 muffins
= 30 ÷ 8
= 3 r 6 (x)

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

If Peter used 16 large boxes,
number of muffins to be packed in small boxes
= 336 - (16 x 18)
= 336 - 288
= 48

Number of small boxes to pack 48 muffins
= 48 ÷ 8
= 6 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Peter used
= 16 + 6
= 22

Answer(s): 22