PSLE
Oliver packed 498 muffins into large and small boxes. He filled each large box with 14 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 Oliver?
To have the least number of boxes, Oliver had to use as many as large boxes as possible.

If Oliver used only large boxes,
number of large boxes used
= 498 ÷ 14
= 35 r 8 (x) There should be no remaining muffins left.

If 35 large boxes are used, there are 8 muffins left, Oliver had to use less large boxes so that the rest of the muffins were packed in small boxes.

If Oliver used 34 large boxes,
number of muffins to be packed in small boxes
= 498 - (34 x 14)
= 498 - 476
= 22

Number of small boxes needed to pack 22 muffins
= 22 ÷ 10
= 2 r 2 (x)

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

If Oliver used 33 large boxes,
number of muffins to be packed in small boxes
= 498 - (33 x 14)
= 498 - 462
= 36

Number of small boxes to pack 36 muffins
= 36 ÷ 10
= 3 r 6 (x)

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

If Oliver used 32 large boxes,
number of muffins to be packed in small boxes
= 498 - (32 x 14)
= 498 - 448
= 50

Number of small boxes to pack 50 muffins
= 50 ÷ 10
= 5 r 0 (✓) There is no remaining muffins left.

Least number of boxes that Oliver used
= 32 + 5
= 37

Answer(s): 37