PSLE
Gabriel packed 344 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 Gabriel?
To have the least number of boxes, Gabriel had to use as many as large boxes as possible.

If Gabriel used only large boxes,
number of large boxes used
= 344 ÷ 18
= 19 r 2 (x) There should be no remaining cupcakes left.

If 19 large boxes are used, there are 2 cupcakes left, Gabriel had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Gabriel used 18 large boxes,
number of cupcakes to be packed in small boxes
= 344 - (18 x 18)
= 344 - 324
= 20

Number of small boxes needed to pack 20 cupcakes
= 20 ÷ 8
= 2 r 4 (x)

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

If Gabriel used 17 large boxes,
number of cupcakes to be packed in small boxes
= 344 - (17 x 18)
= 344 - 306
= 38

Number of small boxes to pack 38 cupcakes
= 38 ÷ 8
= 4 r 6 (x)

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

If Gabriel used 16 large boxes,
number of cupcakes to be packed in small boxes
= 344 - (16 x 18)
= 344 - 288
= 56

Number of small boxes to pack 56 cupcakes
= 56 ÷ 8
= 7 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Gabriel used
= 16 + 7
= 23

Answer(s): 23