PSLE
Elijah packed 352 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 Elijah?
To have the least number of boxes, Elijah had to use as many as large boxes as possible.

If Elijah used only large boxes,
number of large boxes used
= 352 ÷ 12
= 29 r 4 (x) There should be no remaining cupcakes left.

If 29 large boxes are used, there are 4 cupcakes left, Elijah had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Elijah used 28 large boxes,
number of cupcakes to be packed in small boxes
= 352 - (28 x 12)
= 352 - 336
= 16

Number of small boxes needed to pack 16 cupcakes
= 16 ÷ 10
= 1 r 6 (x)

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

If Elijah used 27 large boxes,
number of cupcakes to be packed in small boxes
= 352 - (27 x 12)
= 352 - 324
= 28

Number of small boxes to pack 28 cupcakes
= 28 ÷ 10
= 2 r 8 (x)

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

If Elijah used 26 large boxes,
number of cupcakes to be packed in small boxes
= 352 - (26 x 12)
= 352 - 312
= 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 Elijah used
= 26 + 4
= 30

Answer(s): 30