PSLE
Oscar packed 332 shortbreads into large and small boxes. He filled each large box with 16 shortbreads and each small box with 6 shortbreads. All the boxes were full and no shortbreads were left over. What was the least number of boxes used by Oscar?
To have the least number of boxes, Oscar had to use as many as large boxes as possible.

If Oscar used only large boxes,
number of large boxes used
= 332 ÷ 16
= 20 r 12 (x) There should be no remaining shortbreads left.

If 20 large boxes are used, there are 12 shortbreads left, Oscar had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Oscar used 19 large boxes,
number of shortbreads to be packed in small boxes
= 332 - (19 x 16)
= 332 - 304
= 28

Number of small boxes needed to pack 28 shortbreads
= 28 ÷ 6
= 4 r 4 (x)

There should be no remaining shortbreads left. So, Oscar had to use less large boxes.

If Oscar used 18 large boxes,
number of shortbreads to be packed in small boxes
= 332 - (18 x 16)
= 332 - 288
= 44

Number of small boxes to pack 44 shortbreads
= 44 ÷ 6
= 7 r 2 (x)

There should be no remaining shortbreads left. So, Oscar had to use less large boxes.

If Oscar used 17 large boxes,
number of shortbreads to be packed in small boxes
= 332 - (17 x 16)
= 332 - 272
= 60

Number of small boxes to pack 60 shortbreads
= 60 ÷ 6
= 10 r 0 (✓) There is no remaining shortbreads left.

Least number of boxes that Oscar used
= 17 + 10
= 27

Answer(s): 27