Question

Seven years ago, a mother's age was four times that of her son. This year, the mother's age is 47 years. How old is the son this year?

Answer 1

Let the son's age this year be \( x \).

Seven years ago, the mother's age was \( 47 - 7 = 40 \) years.

According to the problem, seven years ago, the mother's age was four times that of her son's age. Seven years ago, the son's age was \( x - 7 \).

The equation can be set up as follows:

\[
40 = 4(x - 7)
\]

Now, let's solve for \( x \):

\[
40 = 4x - 28
\]

Adding 28 to both sides gives:

\[
40 + 28 = 4x
\]
\[
68 = 4x
\]

Now, divide both sides by 4:

\[
x = \frac{68}{4} = 17
\]

Thus, the son’s age this year is \( \boxed{17} \) years.