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Question 10

Suppose a,b,c are three distinct natural numbers, such that $$3ac=8(a+b)$$. Then, the smallest possible value of $$3a+2b+c$$ is

Correct Answer: 12

Solution

Our task is to minimise $$3a+2b+c$$.

Here, the coefficient for $$c$$ is the minimum.

$$3ac=8(a+b)$$

We know that a, b, and c are natural numbers. So, the product $$ac$$ should definately be a multiple of 8.

Case 1: a = 1, c = 8 and b = 2 $$\Rightarrow$$ 3a+2b+c = 15

Case 2: a = 2, c = 4 and b = 1 $$\Rightarrow$$ 3a+2b+c = 12

So, 12 is the correct answer.

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