Question

The sum of Mr. O'Malley's age and his son's age is 38 years this year. 4 years ago, Mr. O'Malley was 5 times as old as his son. How old is his son this year?

a) 6 years
b) 7 years
c) 8 years
d) 9 years

Answer 1

Mr. O'Malley's son is 9 years old this year. By setting up a system of linear equations based on the information provided, we can solve for the son's age.

Step-by-step explanation:

The student's question revolves around determining the age of Mr. O'Malley's son given specific conditions about their ages. To solve this, we can set up a system of linear equations. Let x be the age of the son this year, and y be the age of Mr. O'Malley this year. According to the problem, we have two equations:

• The sum of Mr. O'Malley's age and his son's age is 38 years: x + y = 38
• Four years ago, Mr. O'Malley was 5 times as old as his son: y - 4 = 5(x - 4)

Solving the first equation for y gives us y = 38 - x. Plugging this into the second equation, we get (38 - x) - 4 = 5(x - 4). Simplifying that results in 34 - x = 5x - 20, which further simplifies to 6x = 54. Dividing both sides by 6 gives us x = 9, which means Mr. O'Malley's son is 9 years old this year.