PSLE
Vaidev packed 342 cupcakes into large and small boxes. He filled each large box with 14 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 Vaidev?
To have the least number of boxes, Vaidev had to use as many as large boxes as possible.

If Vaidev used only large boxes,
number of large boxes used
= 342 ÷ 14
= 24 r 6 (x) There should be no remaining cupcakes left.

If 24 large boxes are used, there are 6 cupcakes left, Vaidev had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Vaidev used 23 large boxes,
number of cupcakes to be packed in small boxes
= 342 - (23 x 14)
= 342 - 322
= 20

Number of small boxes needed to pack 20 cupcakes
= 20 ÷ 6
= 3 r 2 (x)

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

If Vaidev used 22 large boxes,
number of cupcakes to be packed in small boxes
= 342 - (22 x 14)
= 342 - 308
= 34

Number of small boxes to pack 34 cupcakes
= 34 ÷ 6
= 5 r 4 (x)

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

If Vaidev used 21 large boxes,
number of cupcakes to be packed in small boxes
= 342 - (21 x 14)
= 342 - 294
= 48

Number of small boxes to pack 48 cupcakes
= 48 ÷ 6
= 8 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Vaidev used
= 21 + 8
= 29

Answer(s): 29