PSLE
Ken packed 404 cupcakes into large and small boxes. He filled each large box with 14 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 Ken?
To have the least number of boxes, Ken had to use as many as large boxes as possible.

If Ken used only large boxes,
number of large boxes used
= 404 ÷ 14
= 28 r 12 (x) There should be no remaining cupcakes left.

If 28 large boxes are used, there are 12 cupcakes left, Ken had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Ken used 27 large boxes,
number of cupcakes to be packed in small boxes
= 404 - (27 x 14)
= 404 - 378
= 26

Number of small boxes needed to pack 26 cupcakes
= 26 ÷ 10
= 2 r 6 (x)

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

If Ken used 26 large boxes,
number of cupcakes to be packed in small boxes
= 404 - (26 x 14)
= 404 - 364
= 40

Number of small boxes to pack 40 cupcakes
= 40 ÷ 10
= 4 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Ken used
= 26 + 4
= 30

Answer(s): 30