PSLE
Ahmad packed 276 muffins into large and small boxes. He filled each large box with 18 muffins and each small box with 10 muffins. All the boxes were full and no muffins were left over. What was the least number of boxes used by Ahmad?
To have the least number of boxes, Ahmad had to use as many as large boxes as possible.

If Ahmad used only large boxes,
number of large boxes used
= 276 ÷ 18
= 15 r 6 (x) There should be no remaining muffins left.

If 15 large boxes are used, there are 6 muffins left, Ahmad had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Ahmad used 14 large boxes,
number of muffins to be packed in small boxes
= 276 - (14 x 18)
= 276 - 252
= 24

Number of small boxes needed to pack 24 muffins
= 24 ÷ 10
= 2 r 4 (x)

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

If Ahmad used 13 large boxes,
number of muffins to be packed in small boxes
= 276 - (13 x 18)
= 276 - 234
= 42

Number of small boxes to pack 42 muffins
= 42 ÷ 10
= 4 r 2 (x)

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

If Ahmad used 12 large boxes,
number of muffins to be packed in small boxes
= 276 - (12 x 18)
= 276 - 216
= 60

Number of small boxes to pack 60 muffins
= 60 ÷ 10
= 6 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Ahmad used
= 12 + 6
= 18

Answer(s): 18