Step-by-step Solution:

Quick Solution

This age puzzle can be solved easily by translating the statements into a pair of algebraic equations.

1. Set Up the Equations

- Let John's present age be J and Steve's present age be S.

- From the first sentence ("John is 20 years older than Steve"):
J = S + 20 --- (Equation 1)

- In 10 years, their ages will be (J + 10) and (S + 10). From the second sentence ("In 10 years, Steve's age will be half that of John"):
S + 10 = (1/2)(J + 10) --- (Equation 2)

2. Solve for Steve's Age (S)

- Substitute the first equation into the second one to create an equation with only one variable, S:
S + 10 = (1/2)( (S + 20) + 10)

- Now, simplify and solve for S:
S + 10 = (1/2)(S + 30)
- Multiply both sides by 2 to remove the fraction:
2(S + 10) = S + 30
2S + 20 = S + 30
2S - S = 30 - 20
S = 10 years.

3. Verification (Optional)

- If Steve is 10 years old now, then John is 10 + 20 = 30 years old.
- In 10 years, Steve will be 20 and John will be 40.
- 20 is exactly half of 40, so our answer is correct.

Final Answer: Steve's age now is 10.