Question: Jay earns $8 an hour when he works at his uncle’s store. He earns $9 an hour when he does yard work for his neighbor.
Which expression represents the total amount he will earn in a week when he works $u$ hours at his uncle’s store and $v$
hours doing yard work for his neighbor?
○ $8u + 9v$
○ $8(u−v) + 9(v−u)$
○ $17uv$
○ $17(u+v)$
1. **State the problem:** Jay earns $8$ dollars per hour working at his uncle's store and $9$ dollars per hour doing yard work for his neighbor. We want to find an expression for the total amount he earns in a week if he works $u$ hours at the store and $v$ hours doing yard work.
2. **Formula used:** Total earnings = (hourly rate at store) × (hours at store) + (hourly rate for yard work) × (hours doing yard work).
3. **Apply the formula:**
$$\text{Total earnings} = 8u + 9v$$
4. **Check other options:**
- $8(u−v) + 9(v−u)$ simplifies to $8u - 8v + 9v - 9u = (8u - 9u) + (-8v + 9v) = -u + v$, which does not represent total earnings.
- $17uv$ multiplies hours together, which is not how earnings are calculated.
- $17(u+v)$ assumes a combined hourly rate of $17$, which is incorrect since rates differ.
5. **Conclusion:** The correct expression for total earnings is:
$$8u + 9v$$