Question

jeremy is 37 years old; his son raymond is 16. In how many years will raymond be one half of his dad jeremy's age?

Answer 1

Let's denote the number of years from now as \( x \).

Currently:
- Jeremy's age is 37.
- Raymond's age is 16.

In \( x \) years, their ages will be:
- Jeremy's age: \( 37 + x \)
- Raymond's age: \( 16 + x \)

We want to find the value of \( x \) when Raymond's age will be half of Jeremy's age:

\[
16 + x = \frac{1}{2}(37 + x)
\]

To eliminate the fraction, we can multiply both sides by 2:

\[
2(16 + x) = 37 + x
\]

Expanding both sides gives:

\[
32 + 2x = 37 + x
\]

Now, we can isolate \( x \) by subtracting \( x \) from both sides:

\[
32 + x = 37
\]

Next, subtract 32 from both sides:

\[
x = 5
\]

So, in 5 years, Raymond will be half of Jeremy's age.

Let's check the ages in 5 years:
- Jeremy's age will be \( 37 + 5 = 42 \).
- Raymond's age will be \( 16 + 5 = 21 \).

Now, checking the condition:

\[
21 = \frac{1}{2} \times 42
\]

This confirms that in 5 years, Raymond will indeed be half of his dad's age.

Thus, the answer is \( \boxed{5} \).