PSLE
Ben packed 430 cookies into large and small boxes. He filled each large box with 14 cookies and each small box with 8 cookies. All the boxes were full and no cookies were left over. What was the least number of boxes used by Ben?
To have the least number of boxes, Ben had to use as many as large boxes as possible.

If Ben used only large boxes,
number of large boxes used
= 430 ÷ 14
= 30 r 10 (x) There should be no remaining cookies left.

If 30 large boxes are used, there are 10 cookies left, Ben had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Ben used 29 large boxes,
number of cookies to be packed in small boxes
= 430 - (29 x 14)
= 430 - 406
= 24

Number of small boxes needed to pack 24 cookies
= 24 ÷ 8
= 3 (✓) There is no remaining cookies left.

Least number of boxes that Ben used
= 29 + 3
= 32

Answer(s): 32