Ten years ago, Jenny was half the age of Peter. If the sum of their ages now is 50, how old is Peter now?

Let's solve this step by step:

Step 1: Let's denote Jenny's age ten years ago as J and Peter's age ten years ago as P. From the problem, we know that J = 0.5P.

Step 2: We also know that the sum of their current ages is 50. Since ten years have passed, Jenny's current age is J + 10 and Peter's current age is P + 10. So, we have the equation J + 10 + P + 10 = 50.

Step 3: Simplifying the equation from step 2, we get J + P = 30.

Step 4: Now we have a system of two equations: J = 0.5P and J + P = 30. We can substitute the first equation into the second to get 0.5P + P = 30.

Step 5: Simplifying the equation from step 4, we get 1.5P = 30. Solving for P, we find that P = 20.

Step 6: Substituting P = 20 into the equation J = 0.5P, we find that J = 10.

Step 7: Remembering that P and J are the ages of Peter and Jenny ten years ago, we add 10 to each to find their current ages. So, Peter is now 20 + 10 = 30 years old and Jenny is now 10 + 10 = 20 years old.

So, Peter is 30 years old now.