PSLE
Xavier packed 434 cookies into large and small boxes. He filled each large box with 10 cookies and each small box with 4 cookies. All the boxes were full and no cookies were left over. What was the least number of boxes used by Xavier?
To have the least number of boxes, Xavier had to use as many as large boxes as possible.

If Xavier used only large boxes,
number of large boxes used
= 434 ÷ 10
= 43 r 4 (x) There should be no remaining cookies left.

If 43 large boxes are used, there are 4 cookies left, Xavier had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Xavier used 42 large boxes,
number of cookies to be packed in small boxes
= 434 - (42 x 10)
= 434 - 420
= 14

Number of small boxes needed to pack 14 cookies
= 14 ÷ 4
= 3 r 2 (x)

There should be no remaining cookies left. So, Xavier had to use less large boxes.

If Xavier used 41 large boxes,
number of cookies to be packed in small boxes
= 434 - (41 x 10)
= 434 - 410
= 24

Number of small boxes to pack 24 cookies
= 24 ÷ 4
= 6 r 0 (✓) There is no remaining cookies left.

Least number of boxes that Xavier used
= 41 + 6
= 47

Answer(s): 47