A man retires at age so with 605000 in savings. He spends his savings at a steady rate,and after 6 years of retirement he has spent 300,000 Write an equation for the amount the man has in savings When does he have 100,000 in savings?

## Step 1: Calculate the rate of spending.<br />### The man spent $300,000 in 6 years. Therefore, his rate of spending is $\frac{\$300,000}{6 \text{ years}} = \$50,000$ per year.<br /><br />## Step 2: Formulate the equation for savings.<br />### Let $S$ be the savings and $t$ be the time in years since retirement. The initial savings is $605,000. The rate of spending is $50,000 per year. So, the equation is $S = 605000 - 50000t$.<br /><br />## Step 3: Calculate the time when savings reach $100,000.<br />### We want to find $t$ when $S = 100,000$. Substitute $S = 100,000$ into the equation: $100000 = 605000 - 50000t$. Solving for $t$: $50000t = 605000 - 100000$, so $50000t = 505000$. Thus, $t = \frac{505000}{50000} = 10.1$ years.