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 \( \boxed{5} \).
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