Question: User: Barba is 30 years older than Joan. in 10 years time, the ratio of their age will be 5:2. how old is each now?
1. **State the problem:**
Barba is 30 years older than Joan. In 10 years, the ratio of their ages will be 5:2. We need to find their current ages.
2. **Define variables:**
Let $J$ be Joan's current age.
Then Barba's current age is $J + 30$.
3. **Write the ratio equation for ages in 10 years:**
In 10 years, Joan's age will be $J + 10$ and Barba's age will be $J + 30 + 10 = J + 40$.
The ratio given is $$\frac{J + 40}{J + 10} = \frac{5}{2}$$
4. **Set up the equation and solve:**
$$2(J + 40) = 5(J + 10)$$
$$2J + 80 = 5J + 50$$
5. **Isolate $J$:**
$$80 - 50 = 5J - 2J$$
$$30 = 3J$$
$$J = \frac{30}{3}$$
$$J = 10$$
6. **Find Barba's age:**
$$J + 30 = 10 + 30 = 40$$
7. **Answer:**
Joan is currently 10 years old.
Barba is currently 40 years old.