PSLE
Cody packed 270 cupcakes into large and small boxes. He filled each large box with 12 cupcakes and each small box with 10 cupcakes. All the boxes were full and no cupcakes were left over. What was the least number of boxes used by Cody?
To have the least number of boxes, Cody had to use as many as large boxes as possible.

If Cody used only large boxes,
number of large boxes used
= 270 ÷ 12
= 22 r 6 (x) There should be no remaining cupcakes left.

If 22 large boxes are used, there are 6 cupcakes left, Cody had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Cody used 21 large boxes,
number of cupcakes to be packed in small boxes
= 270 - (21 x 12)
= 270 - 252
= 18

Number of small boxes needed to pack 18 cupcakes
= 18 ÷ 10
= 1 r 8 (x)

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

If Cody used 20 large boxes,
number of cupcakes to be packed in small boxes
= 270 - (20 x 12)
= 270 - 240
= 30

Number of small boxes to pack 30 cupcakes
= 30 ÷ 10
= 3 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Cody used
= 20 + 3
= 23

Answer(s): 23