PSLE
Justin packed 260 scones into large and small boxes. He filled each large box with 16 scones and each small box with 12 scones. All the boxes were full and no scones 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
= 260 ÷ 16
= 16 r 4 (x) There should be no remaining scones left.

If 16 large boxes are used, there are 4 scones left, Justin had to use less large boxes so that the rest of the scones were packed in small boxes.

If Justin used 15 large boxes,
number of scones to be packed in small boxes
= 260 - (15 x 16)
= 260 - 240
= 20

Number of small boxes needed to pack 20 scones
= 20 ÷ 12
= 1 r 8 (x)

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

If Justin used 14 large boxes,
number of scones to be packed in small boxes
= 260 - (14 x 16)
= 260 - 224
= 36

Number of small boxes to pack 36 scones
= 36 ÷ 12
= 3 r 0 (✓) There is no remaining scones left.

Least number of boxes that Justin used
= 14 + 3
= 17

Answer(s): 17