Question: Grace has some baskets of apples. Each basket contain 10 apples. When Grace repacks all the apples into baskets of 9 apples she will need 1 more basket. How many apples are there altogether?
1. **State the problem:** Grace has some baskets each containing $10$ apples. When she repacks the apples into baskets of $9$ apples, she needs $1$ more basket than before. We need to find the total number of apples.
2. **Define variables:** Let $n$ be the number of baskets originally.
3. **Express total apples:** Total apples $= 10n$.
4. **Repacking condition:** When repacked into baskets of $9$ apples, the number of baskets needed is $n + 1$.
5. **Write equation for total apples:** Total apples $= 9(n + 1)$.
6. **Set equal total apples:**
$$10n = 9(n + 1)$$
7. **Expand right side:**
$$10n = 9n + 9$$
8. **Subtract $9n$ from both sides:**
$$10n - 9n = 9$$
$$\cancel{10n} - \cancel{9n} = 9$$
9. **Simplify:**
$$n = 9$$
10. **Calculate total apples:**
$$10n = 10 \times 9 = 90$$
**Answer:** There are $90$ apples altogether.