Question

The number of solution to the equation $2a+3b+6c=60,$ where $a,b,c\in N$ , is equal to

Answer 1

Answer: 36

$2a+3b+6c=60$
Note that $3b,6c,60$ are divisible by $3,$ hence $2a$ is divisible by $3$
Similarly $2a,6c,60$ are even numbers hence $3b$ is an even number
Therefore $a=3k_1,b=2k_2$
So the equation reduces to $k_1+k_2+C=10,\forall k_1,k_2,C\in N$
Hence, the number of solutions $=\_{}^9{C}_2=36$