Ten years ago, Jenny was half the age of Peter. If the sum of their ages now is 50, how old is Peter now? Options 40 years 30 years 25 years 35 years

Let's denote Jenny's current age as $J$ and Peter's current age as $P$.

1. According to the problem, ten years ago, Jenny was half the age of Peter. This can be written as: $J - 10 = \frac{1}{2}(P - 10)$

2. The problem also states that the sum of their current ages is 50: $J + P = 50$

3. We now have two equations: $J - 10 = \frac{1}{2}(P - 10)$ $J + P = 50$

4. Let's solve the first equation for $J$: $J - 10 = \frac{1}{2}P - 5$ $J = \frac{1}{2}P + 5$

5. Substitute $J$ from the above equation into the second equation: $\left(\frac{1}{2}P + 5\right) + P = 50$ $\frac{1}{2}P + 5 + P = 50$ $\frac{3}{2}P + 5 = 50$

6. Subtract 5 from both sides: $\frac{3}{2}P = 45$

7. Multiply both sides by $\frac{2}{3}$: $P = 30$

So, Peter is now 30 years old. The correct option is:

30 years