A box contains 42 red counters, 90 yellow counters and no other counters. A group of students share these counters between them so that they each receive the
same number of red counters and the same number of yellow counters.
There are no counters left over,
How many students could be in the group?
Give all possible answers and show your reasoning.

Please help

i think is g(1)=-1.

hope that i can

step-by-step explanation:

; fx

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