This year the Sum of Mr. Bellinis age and his son's age his son's age is 38 years. 4 years ago, Mr. Bellini was 5 times as old as his son. How old is his son this year? How old is Mr. Bellini this year?
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To find the ages of Mr. Bellini and his son, we can use algebraic equations. Let's represent Mr. Bellini's current age as "B" and his son's current age as "S".
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.