PSLE
Riordan packed 394 cupcakes into large and small boxes. He filled each large box with 20 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 Riordan?
To have the least number of boxes, Riordan had to use as many as large boxes as possible.

If Riordan used only large boxes,
number of large boxes used
= 394 ÷ 20
= 19 r 14 (x) There should be no remaining cupcakes left.

If 19 large boxes are used, there are 14 cupcakes left, Riordan had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Riordan used 18 large boxes,
number of cupcakes to be packed in small boxes
= 394 - (18 x 20)
= 394 - 360
= 34

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

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

If Riordan used 17 large boxes,
number of cupcakes to be packed in small boxes
= 394 - (17 x 20)
= 394 - 340
= 54

Number of small boxes to pack 54 cupcakes
= 54 ÷ 6
= 9 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Riordan used
= 17 + 9
= 26

Answer(s): 26