If (𝟓𝒂−𝟑𝒃)∶(𝟒𝒂−𝟐𝒃)=𝟐∶𝟑 then a : b is equal to:Options5 : 72 : 33 : 45 : 8

The given equation is (5a - 3b) : (4a - 2b) = 2 : 3.

Step 1: We can simplify the equation by dividing both sides of the equation by 2. This gives us:

(5a - 3b) / (4a - 2b) = 2/3

Step 2: Cross multiply to get rid of the fraction:

3*(5a - 3b) = 2*(4a - 2b)

Step 3: Distribute on both sides:

15a - 9b = 8a - 4b

Step 4: Rearrange the equation to isolate 'a' terms on one side and 'b' terms on the other:

15a - 8a = 4b + 9b

Step 5: Simplify to find the ratio of 'a' to 'b':

7a = 13b

So, a : b = 13 : 7.

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