Select the correct answerIf 𝒂:𝒃=𝟑:𝟐, then (𝟓𝒂+𝟐𝒃):(𝟑𝒂+𝟒𝒃) is equal to?

Sure, here is the step by step solution:

Given that a:b = 3:2, we can say a = 3k and b = 2k for some constant k.

Now, we need to find the ratio (5a + 2b) : (3a + 4b).

Substitute a = 3k and b = 2k into the equation.

So, (5a + 2b) : (3a + 4b) becomes (53k + 22k) : (33k + 42k).

This simplifies to (15k + 4k) : (9k + 8k), which further simplifies to 19k : 17k.

Since k is a common factor, we can cancel it out to get the final ratio 19:17.

So, if a:b = 3:2, then (5a + 2b) : (3a + 4b) is equal to 19:17.