PSLE
Howard packed 292 tarts into large and small boxes. He filled each large box with 10 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 Howard?
To have the least number of boxes, Howard had to use as many as large boxes as possible.

If Howard used only large boxes,
number of large boxes used
= 292 ÷ 10
= 29 r 2 (x) There should be no remaining tarts left.

If 29 large boxes are used, there are 2 tarts left, Howard had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Howard used 28 large boxes,
number of tarts to be packed in small boxes
= 292 - (28 x 10)
= 292 - 280
= 12

Number of small boxes needed to pack 12 tarts
= 12 ÷ 8
= 1 r 4 (x)

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

If Howard used 27 large boxes,
number of tarts to be packed in small boxes
= 292 - (27 x 10)
= 292 - 270
= 22

Number of small boxes to pack 22 tarts
= 22 ÷ 8
= 2 r 6 (x)

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

If Howard used 26 large boxes,
number of tarts to be packed in small boxes
= 292 - (26 x 10)
= 292 - 260
= 32

Number of small boxes to pack 32 tarts
= 32 ÷ 8
= 4 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Howard used
= 26 + 4
= 30

Answer(s): 30