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

Question

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

MARKS App · Accepted Answer

2 a + 3 b + 6 c = 60 Note that 3 b , 6 c , 60 are divisible by 3 , hence 2 a is divisible by 3 Similarly 2 a , 6 c , 60 are even numbers hence 3 b is an even number Therefore a = 3 k 1 , b = 2 k 2 So the equation reduces to k 1 + k 2 + C = 10 , ∀ k 1 , k 2 , C ∈ N Hence, the number of solutions = C 2 = 36 9

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