PSLE
Billy packed 414 cupcakes into large and small boxes. He filled each large box with 12 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 Billy?
To have the least number of boxes, Billy had to use as many as large boxes as possible.

If Billy used only large boxes,
number of large boxes used
= 414 ÷ 12
= 34 r 6 (x) There should be no remaining cupcakes left.

If 34 large boxes are used, there are 6 cupcakes left, Billy had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Billy used 33 large boxes,
number of cupcakes to be packed in small boxes
= 414 - (33 x 12)
= 414 - 396
= 18

Number of small boxes needed to pack 18 cupcakes
= 18 ÷ 6
= 3 (✓) There is no remaining cupcakes left.

Least number of boxes that Billy used
= 33 + 3
= 36

Answer(s): 36