Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

Options

A. 38
B. 33
C. 22
D. 16

Explanation

To solve the problem, we need to determine how many hours Ken must work at the new rate of $10 per hour in order to save at least $270 for the week.

### Step-by-Step Solution:

1. **Calculate Earnings for the First 10 Hours:**
Ken earns $8 per hour for the first 10 hours.
\[ \text{Earnings from first 10 hours} = 8 \times 10 = 80 \text{ dollars} \]

**Hint:** Multiply the hourly wage by the number of hours worked to find total earnings.

2. **Define the Total Hours Worked:**
Let \( X \) be the total number of hours Ken works in the week. Therefore, the hours worked after the first 10 hours is \( X - 10 \).

**Hint:** Use a variable to represent the total hours worked for easier calculations.

3. **Calculate Earnings for the Remaining Hours:**
Ken earns $10 per hour for the remaining \( X - 10 \) hours.
\[ \text{Earnings from remaining hours} = 10 \times (X - 10) \]

**Hint:** Again, multiply the hourly wage by the number of hours worked to find total earnings for the remaining hours.

4. **Total Earnings for the Week:**
The total earnings for the week can be expressed as:
\[ \text{Total Earnings} = 80 + 10(X - 10) \]

**Hint:** Combine the earnings from both parts of the week to find total earnings.

5. **Calculate Total Savings:**
Ken saves 90% of his total earnings. Therefore, his savings can be expressed as:
\[ \text{Savings} = 0.9 \times (80 + 10(X - 10)) \]

**Hint:** Remember to multiply the total earnings by the savings percentage to find total savings.

6. **Set Up the Inequality for Savings:**
We want Ken's savings to be at least $270:
\[ 0.9 \times (80 + 10(X - 10)) \geq 270 \]

**Hint:** Set up an inequality to express the requirement for savings.

7. **Solve the Inequality:**
First, simplify the inequality:
\[ 0.9 \times (80 + 10X - 100) \geq 270 \]
\[ 0.9 \times (10X - 20) \geq 270 \]
Divide both sides by 0.9:
\[ 10X - 20 \geq 300 \]
Add 20 to both sides:
\[ 10X \geq 320 \]
Divide by 10:
\[ X \geq 32 \]

**Hint:** Isolate the variable to find the minimum total hours required.

8. **Calculate Hours Worked After the First 10:**
Since Ken worked a total of \( X \) hours, the hours he must work after the first 10 hours is:
\[ X - 10 \geq 32 - 10 \]
\[ X - 10 \geq 22 \]

**Hint:** Subtract the hours already worked from the total to find the remaining hours.

### Conclusion:
Ken must work at least **22 hours** for the rest of the week to save at least $270.