PSLE
Simon packed 460 cupcakes into large and small boxes. He filled each large box with 18 cupcakes and each small box with 8 cupcakes. All the boxes were full and no cupcakes were left over. What was the least number of boxes used by Simon?
To have the least number of boxes, Simon had to use as many as large boxes as possible.

If Simon used only large boxes,
number of large boxes used
= 460 ÷ 18
= 25 r 10 (x) There should be no remaining cupcakes left.

If 25 large boxes are used, there are 10 cupcakes left, Simon had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Simon used 24 large boxes,
number of cupcakes to be packed in small boxes
= 460 - (24 x 18)
= 460 - 432
= 28

Number of small boxes needed to pack 28 cupcakes
= 28 ÷ 8
= 3 r 4 (x)

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

If Simon used 23 large boxes,
number of cupcakes to be packed in small boxes
= 460 - (23 x 18)
= 460 - 414
= 46

Number of small boxes to pack 46 cupcakes
= 46 ÷ 8
= 5 r 6 (x)

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

If Simon used 22 large boxes,
number of cupcakes to be packed in small boxes
= 460 - (22 x 18)
= 460 - 396
= 64

Number of small boxes to pack 64 cupcakes
= 64 ÷ 8
= 8 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Simon used
= 22 + 8
= 30

Answer(s): 30