PSLE
Sam packed 374 cupcakes into large and small boxes. He filled each large box with 16 cupcakes and each small box with 6 cupcakes. All the boxes were full and no cupcakes were left over. What was the least number of boxes used by Sam?
To have the least number of boxes, Sam had to use as many as large boxes as possible.

If Sam used only large boxes,
number of large boxes used
= 374 ÷ 16
= 23 r 6 (x) There should be no remaining cupcakes left.

If 23 large boxes are used, there are 6 cupcakes left, Sam had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Sam used 22 large boxes,
number of cupcakes to be packed in small boxes
= 374 - (22 x 16)
= 374 - 352
= 22

Number of small boxes needed to pack 22 cupcakes
= 22 ÷ 6
= 3 r 4 (x)

There should be no remaining cupcakes left. So, Sam had to use less large boxes.

If Sam used 21 large boxes,
number of cupcakes to be packed in small boxes
= 374 - (21 x 16)
= 374 - 336
= 38

Number of small boxes to pack 38 cupcakes
= 38 ÷ 6
= 6 r 2 (x)

There should be no remaining cupcakes left. So, Sam had to use less large boxes.

If Sam used 20 large boxes,
number of cupcakes to be packed in small boxes
= 374 - (20 x 16)
= 374 - 320
= 54

Number of small boxes to pack 54 cupcakes
= 54 ÷ 6
= 9 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Sam used
= 20 + 9
= 29

Answer(s): 29