Milk starts a job at which his starting salary is `$25500` per year. He expects that his salary will increase by a constnat dollar amount annually. In 12 years, his salary will be doulb ehis starting salary. Assuming salary increases take place only at the eand of a full year, how many years must Malik wait until his salary is at least `$40,000` annually ?

Explanation

To solve the problem step by step, we need to determine how long Malik must wait until his salary reaches at least $40,000 annually, given his starting salary and the rate of increase.

### Step 1: Identify the starting salary and the target salary
- Malik's starting salary is $25,500.
- He wants his salary to be at least $40,000.

### Step 2: Determine the salary after 12 years
- After 12 years, Malik's salary will double his starting salary.
- Therefore, the salary after 12 years = 2 × $25,500 = $51,000.

### Step 3: Calculate the annual increase in salary
- The total increase in salary over 12 years = $51,000 - $25,500 = $25,500.
- The annual increase = Total increase / Number of years = $25,500 / 12 = $2,125.

### Step 4: Set up the equation for the salary after n years
- Malik's salary after n years can be expressed as:
\[ \text{Salary after n years} = \text{Starting salary} + n \times \text{Annual increase} \]
\[ \text{Salary after n years} = 25,500 + n \times 2,125 \]

### Step 5: Set the equation to find when the salary is at least $40,000
- We need to find n such that:
\[ 25,500 + n \times 2,125 \geq 40,000 \]

### Step 6: Solve for n
- Rearranging the equation:
\[ n \times 2,125 \geq 40,000 - 25,500 \]
\[ n \times 2,125 \geq 14,500 \]
- Dividing both sides by 2,125:
\[ n \geq \frac{14,500}{2,125} \approx 6.82 \]

### Step 7: Determine the whole number of years
- Since salary increases only occur at the end of the year, we round up to the nearest whole number.
- Therefore, Malik must wait at least **7 years** for his salary to reach at least $40,000.

### Conclusion
Malik must wait **7 years** until his salary is at least $40,000 annually.

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