Question

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets.(1) What is your variable and what does it represent?(2) Write your inequality : (3) Solve your inequality : (4) Explain ehat your solution means to keith : (5) Keith wants to withdraw money for 15 weeks. Is this possible? please explain : (6) If keith withdraws money for 20 week how much would be in his savings?

Answer 1

(1) Let's define the next variable,

x : number of weeks

(2) the inequality is:

500 - 25x ≥ 200

that is, he starts with $500, after each week he spends $25, so after x weeks he will spend 25x dollars; the remaining money has to be at least 200

(3) 500 - 25x ≥ 200

-25x ≥ 200 - 500

-25x ≥ -300

x ≤ (-300)/(-25)

x ≤ 12

(4) The solution means that Keith can spend $25 each week for 12 weeks

(5) Is not possible, because he will end with less than $200

(6) Replacing x = 20 in the next equation, we get:

500 - 25x =

= 500 - 25(20) =

= 500 - 500

= 0

It would be $0 in his savings