Question

Brian's Orchard supplies apples to markets in Albany. The apples can be packed into a large bag that holds 9 apples or a small bag that holds 6 apples.

The orchard needs to fill an order for 156 apples using both large and small bags. What is the least number of each type of bag that could be used if each bag is completely filled?

Answer 1

The question makes no sense to me, i found the minimum number of TOTAL bags, but i don't know how to find the minimum of individuals

Answer 2

say \(b\) is the number of big bags and \(s\) the number of small bags
\[9b + 6s = 156\]

you want to solve above equation in nonnegative integers

Answer 3

exactly, yes..... and this is supposedly a 4th grade problem so the solution shouldn't really involve math that is too complex like, say, diophantine equations, etc

Answer 4

ohk i was about to suggest diophantine equation haha

maybe start by dividing 3 through out

Answer 5

i was thinking that maybe it was a typo and they meant to say minimum TOTAL, but not sure

Answer 6

3b + 2s = 52

Answer 7

i see... it should be "minimum TOTAL number of bags"

must be a typo

Answer 8

okay thanks

Answer 9

did you get 10 for the "minimum total bags" ?

Answer 10

um, no actually i got 18, because 16 is the greatest possible number of large bags, and 2 the least number of small bags (because we want to maximize large bags and minimize small bags, so as to decrease overall number of bags). Is that correct?

Answer 11

Oh yes right, im also getting 16 big bags and 2 small bags

Answer 12

great, thanks

Answer 13

np:)