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

Question

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

Knowee AI · Accepted Answer