Question

The total age of a woman and her son is 51 years. Three years ago, the wom was eight times as old as her son. How old is her son now?

Answer 1

The total age of the woman and her son is 51 years, and three years ago, the woman was eight times as old as her son. By setting up a system of equations and solving, we find that the son's current age is 8 years old.

Step-by-step explanation:

Finding the Ages of a Woman and Her Son

The problem states that the total age of a woman and her son is 51 years. Three years ago, the woman was eight times as old as her son. To find the current age of the son, we can set up a system of equations based on the information given.

Let's denote the current age of the woman as w and the current age of the son as s. Therefore, we have:

• w + s = 51 (The total age of the woman and her son is 51 years)
• w - 3 = 8(s - 3) (Three years ago, the woman was eight times as old as her son)

Using substitution or elimination methods to solve this system of equations, we find:

1. Solve the second equation for w: w = 8s - 24 + 3
2. Substitute w from the second equation into the first equation, yielding 8s - 24 + 3 + s = 51
3. Combine like terms to solve for s: 9s - 21 = 51
4. Add 21 to both sides: 9s = 72
5. Divide by 9: s = 8

The son is currently 8 years old.