Question: Jill and Brian divided up $1900 between two investment accounts. Jill's account earns 4% interest and Brian's earns 3%. If their combined interest earns them $70, then how much was originally invested in each account?
1. **State the problem:**
Jill and Brian together invested $1900 in two accounts. Jill's account earns 4% interest, Brian's earns 3%, and the total interest earned is $70. We need to find how much each invested.
2. **Define variables:**
Let Jill's investment be $x$ dollars.
Then Brian's investment is $1900 - x$ dollars.
3. **Write the interest equation:**
Interest from Jill's account: $0.04x$
Interest from Brian's account: $0.03(1900 - x)$
Total interest: $70$
So, the equation is:
$$0.04x + 0.03(1900 - x) = 70$$
4. **Simplify the equation:**
$$0.04x + 0.03 \times 1900 - 0.03x = 70$$
$$0.04x + 57 - 0.03x = 70$$
5. **Combine like terms:**
$$0.04x - 0.03x + 57 = 70$$
$$0.01x + 57 = 70$$
6. **Isolate $x$:**
$$0.01x = 70 - 57$$
$$0.01x = 13$$
7. **Solve for $x$:**
$$x = \frac{13}{0.01}$$
$$x = 1300$$
8. **Find Brian's investment:**
$$1900 - 1300 = 600$$
9. **Answer:**
Jill invested $1300$ and Brian invested $600$.
This matches the first choice: Jill's had $1300$ and Brian's had $600$.