## A man retires at age 50 with \$605,000 in savings. He spends his savings at a steady rate, and after 6 years of retirement, he has spent \$300

Question

A man retires at age 50 with \$605,000 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 will he have \$100,000 in savings?

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1. Since it states that he “spends his savings at a steady rate,” we can assume this is a linear equation.

What we know is that he started with \$605,000 and after 6 years, he used \$300,000. So, we just subtract what he had originally by what he used and get \$305,000. We can now make the equation as follows:

300,000=6x, where x is the amount of money he spent in one year. This equation simplifies to x=50,000, which is the amount of money he spent in one year.

Since the question asks us to tell how long it will take him to reach \$100,000 in savings, we can make the equation using previous value we have found:

100,000=305,000-50,000x, where x is the number of years passed.

So, this equation solves to -205,000=-50,000x, or x=4.1

I’m not sure how you want to express your answer, but it took him 4.1 years on top of the 6 years already passed to reach \$100,000. This mean 10.1 years in total.

Hope this helps!