A shop sells boxes of chocolate. In total there are 252 dark chocolate and 180 milk chocolates. if every box is identical, how many boxes could there be?

12 boxes.

Step-by-step explanation:

We need to find the greatest common factor of 251 and 180:

First find the prime factors :

252 = 2*2*3*3*7

180 =  2*2*3*3*5

So the GCF = 2*2*3*3 = 36.

So id each box is identical, there could be 7 boxes of dark chocolates and 5 boxes of milk chocolates each containing 36 chocolates.

Total number of boxes = 12.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb