fish when they went on vacation. He spent $$ \$ 13 $$ of his earnings on a book and $$ \$ 9 $$ on some art supplies. Afterward, he had at most $$ \$ 10 $$ left. Write an inequality to represent how much Diego's neighbors paid him. Then solve the inequality

Question

UpStudy AI · Accepted Answer

Let's break down the problem step by step to formulate and solve the inequality.

### **Step 1: Define the Variable**
Let $$ x $$ represent the total amount of money Diego's neighbors paid him.

### **Step 2: Account for Expenses**
Diego spent:
- $$ \$13 $$ on a book
- $$ \$9 $$ on art supplies

**Total Expenses:**  
$$ 13 + 9 = \$22 $$

### **Step 3: Set Up the Inequality**
After spending $$ \$22 $$, Diego had **at most** $$ \$10 $$ left. This means the remaining amount is **less than or equal to** $$ \$10 $$.

The relationship can be expressed as:
$$ \text{Total Earnings} - \text{Total Expenses} \leq \text{Amount Left} $$

Substituting the known values:
$$ x - 22 \leq 10 $$

### **Step 4: Solve the Inequality**
To find the maximum amount Diego could have been paid ($$ x $$), solve for $$ x $$:

1. **Add 22 to both sides of the inequality:**
   $$
   x - 22 + 22 \leq 10 + 22
   $$
   $$
   x \leq 32
   $$

### **Conclusion**
Diego's neighbors paid him **at most** $$ \$32 $$.

### **Final Answer**
**Inequality:**  
$$ x - 13 - 9 \leq 10 $$

**Solution:**  
$$ x \leq 32 $$

Thus, Diego's neighbors paid him **a maximum of \$32**.
Diego's neighbors paid him at most \$32. **Inequality:** $$ x - 13 - 9 \leq 10 $$ **Solution:** $$ x \leq 32 $$

fish when they went on vacation. He spent \( \$ 13 \) of his earnings on a book and \( \$ 9 \) on some art supplies. Afterward, he had at most \( \$ 10 \) left. Write an inequality to represent how much Diego's neighbors paid him. Then solve the inequality

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions