PSLE
Justin packed 424 tarts into large and small boxes. He filled each large box with 18 tarts and each small box with 8 tarts. All the boxes were full and no tarts were left over. What was the least number of boxes used by Justin?
To have the least number of boxes, Justin had to use as many as large boxes as possible.

If Justin used only large boxes,
number of large boxes used
= 424 ÷ 18
= 23 r 10 (x) There should be no remaining tarts left.

If 23 large boxes are used, there are 10 tarts left, Justin had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Justin used 22 large boxes,
number of tarts to be packed in small boxes
= 424 - (22 x 18)
= 424 - 396
= 28

Number of small boxes needed to pack 28 tarts
= 28 ÷ 8
= 3 r 4 (x)

There should be no remaining tarts left. So, Justin had to use less large boxes.

If Justin used 21 large boxes,
number of tarts to be packed in small boxes
= 424 - (21 x 18)
= 424 - 378
= 46

Number of small boxes to pack 46 tarts
= 46 ÷ 8
= 5 r 6 (x)

There should be no remaining tarts left. So, Justin had to use less large boxes.

If Justin used 20 large boxes,
number of tarts to be packed in small boxes
= 424 - (20 x 18)
= 424 - 360
= 64

Number of small boxes to pack 64 tarts
= 64 ÷ 8
= 8 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Justin used
= 20 + 8
= 28

Answer(s): 28