PSLE
Daniel packed 486 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 Daniel?
To have the least number of boxes, Daniel had to use as many as large boxes as possible.

If Daniel used only large boxes,
number of large boxes used
= 486 ÷ 16
= 30 r 6 (x) There should be no remaining shortbreads left.

If 30 large boxes are used, there are 6 shortbreads left, Daniel had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Daniel used 29 large boxes,
number of shortbreads to be packed in small boxes
= 486 - (29 x 16)
= 486 - 464
= 22

Number of small boxes needed to pack 22 shortbreads
= 22 ÷ 6
= 3 r 4 (x)

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

If Daniel used 28 large boxes,
number of shortbreads to be packed in small boxes
= 486 - (28 x 16)
= 486 - 448
= 38

Number of small boxes to pack 38 shortbreads
= 38 ÷ 6
= 6 r 2 (x)

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

If Daniel used 27 large boxes,
number of shortbreads to be packed in small boxes
= 486 - (27 x 16)
= 486 - 432
= 54

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

Least number of boxes that Daniel used
= 27 + 9
= 36

Answer(s): 36