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From the given information, we know that the sum of Mr. Bellini's age and his son's age is 38 years. So, the first equation is:
B + S = 38 ---- Equation 1
We also know that 4 years ago, Mr. Bellini was 5 times as old as his son. This can be written as an equation:
B - 4 = 5(S - 4) ---- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2). We can solve this system to find the values of B and S.
First, let's simplify Equation 2:
B - 4 = 5S - 20
Next, let's rearrange Equation 1 to solve for B:
B = 38 - S
Now, substitute B in Equation 2 with the value from Equation 1:
38 - S - 4 = 5S - 20
Combine like terms:
34 - S = 5S - 20
Add S to both sides of the equation:
34 = 6S - 20
Add 20 to both sides of the equation:
54 = 6S
Divide both sides of the equation by 6:
S = 9
So, the son's age this year is 9 years.
To find Mr. Bellini's age, substitute the value of S back into Equation 1:
B + 9 = 38
Subtract 9 from both sides of the equation:
B = 38 - 9
B = 29
Therefore, Mr. Bellini's age this year is 29 years.