PSLE
Gabriel packed 258 muffins into large and small boxes. He filled each large box with 14 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 Gabriel?
To have the least number of boxes, Gabriel had to use as many as large boxes as possible.

If Gabriel used only large boxes,
number of large boxes used
= 258 ÷ 14
= 18 r 6 (x) There should be no remaining muffins left.

If 18 large boxes are used, there are 6 muffins left, Gabriel had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Gabriel used 17 large boxes,
number of muffins to be packed in small boxes
= 258 - (17 x 14)
= 258 - 238
= 20

Number of small boxes needed to pack 20 muffins
= 20 ÷ 8
= 2 r 4 (x)

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

If Gabriel used 16 large boxes,
number of muffins to be packed in small boxes
= 258 - (16 x 14)
= 258 - 224
= 34

Number of small boxes to pack 34 muffins
= 34 ÷ 8
= 4 r 2 (x)

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

If Gabriel used 15 large boxes,
number of muffins to be packed in small boxes
= 258 - (15 x 14)
= 258 - 210
= 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 Gabriel used
= 15 + 6
= 21

Answer(s): 21