Final answer:
William needs to save $5 per week to reach his savings goal of $200. Starting with $60, defining the variable w as the number of weeks, he will need a minimum of 28 weeks to reach his goal since 60 + 5w ≥ 200, which simplifies to w ≥ 28.
Step-by-step explanation:
To calculate the number of weeks it will take for William to reach his savings goal of at least $200 by investing $5 of his weekly allowance, we will define the variable w as the number of weeks required. William currently has $60 in his savings account. Since he saves $5 per week, the total savings after w weeks will be $60 + $5w. He wants to save at least $200, so we need to solve the inequality $60 + $5w ≥ $200.
To find w, we subtract $60 from both sides of the inequality to get $5w ≥ $140. Then, we divide both sides by $5 to get w ≥ 28. Therefore, it will take William at least 28 weeks to save at least $200 at the rate of $5 per week.
The power of compound interest is not directly applicable to William's situation since he is making regular savings contributions without any interest being applied to his savings. Nevertheless, the concept of saving consistently over time is similar to the principle of early savings which, if combined with compound interest, can result in substantial growth of one's investments.