PSLE
Brandon packed 456 cupcakes into large and small boxes. He filled each large box with 16 cupcakes and each small box with 12 cupcakes. All the boxes were full and no cupcakes were left over. What was the least number of boxes used by Brandon?
To have the least number of boxes, Brandon had to use as many as large boxes as possible.

If Brandon used only large boxes,
number of large boxes used
= 456 ÷ 16
= 28 r 8 (x) There should be no remaining cupcakes left.

If 28 large boxes are used, there are 8 cupcakes left, Brandon had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Brandon used 27 large boxes,
number of cupcakes to be packed in small boxes
= 456 - (27 x 16)
= 456 - 432
= 24

Number of small boxes needed to pack 24 cupcakes
= 24 ÷ 12
= 2 (✓) There is no remaining cupcakes left.

Least number of boxes that Brandon used
= 27 + 2
= 29

Answer(s): 29