PSLE
Rael packed 276 shortbreads into large and small boxes. He filled each large box with 16 shortbreads and each small box with 4 shortbreads. All the boxes were full and no shortbreads were left over. What was the least number of boxes used by Rael?
To have the least number of boxes, Rael had to use as many as large boxes as possible.

If Rael used only large boxes,
number of large boxes used
= 276 ÷ 16
= 17 r 4 (x) There should be no remaining shortbreads left.

If 17 large boxes are used, there are 4 shortbreads left, Rael had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Rael used 16 large boxes,
number of shortbreads to be packed in small boxes
= 276 - (16 x 16)
= 276 - 256
= 20

Number of small boxes needed to pack 20 shortbreads
= 20 ÷ 4
= 5 (✓) There is no remaining shortbreads left.

Least number of boxes that Rael used
= 16 + 5
= 21

Answer(s): 21