If 𝒂:𝒃=𝟑:𝟐, then (𝟓𝒂+𝟐𝒃):(𝟑𝒂+𝟒𝒃) is equal to?Options16:158:719:1717:14

To solve this problem, we first need to understand that the ratio a:b = 3:2 means that a/b = 3/2.

We are asked to find the ratio (5a+2b):(3a+4b).

Step 1: Substitute a/b = 3/2 into the equation (5a+2b):(3a+4b).

Step 2: This gives us (5*(3/2)b + 2b) : (3(3/2)*b + 4b).

Step 3: Simplify the equation to get (15/2)*b + 2b : (9/2)*b + 4b.

Step 4: Further simplify to get (7.5b + 2b) : (4.5b + 4b).

Step 5: This simplifies to 9.5b : 8.5b.

Step 6: Since the b's cancel out in a ratio, we are left with 9.5 : 8.5.

Step 7: Simplify the ratio to get 19:17.

So, the ratio (5a+2b):(3a+4b) is equal to 19:17.