Question

You are on a diet to lose 15 pounds in 8 weeks. The first week you lost 3 pounds, and then you lost 2 pounds per week for each of the next 3 weeks. The fifth week showed a gain of 2 pounds, but the sixth and seventh each had a loss of 2 pounds. You are beginning your eighth week. How many pounds do you need to lose in the eighth week in order to meet your goal?

Short answer

Answer: 4 pounds.

Step-by-step solution

Summing up the weight change for the first 7 weeks

Add the weight change for each week: Week 1: -3 pounds (lost) Week 2: -2 pounds (lost) Week 3: -2 pounds (lost) Week 4: -2 pounds (lost) Week 5: +2 pounds (gained) Week 6: -2 pounds (lost) Week 7: -2 pounds (lost) Add all the weight change together: -3 + (-2) + (-2) + (-2) + 2 + (-2) + (-2) = -11 pounds. By the end of the seventh week, a total of 11 pounds of weight has been lost.

Calculate how much weight is left to lose in the eighth week

Subtract the weight lost so far from the target weight loss of 15 pounds: Required weight loss = Target weight loss - Weight lost so far Required weight loss = 15 pounds - 11 pounds Required weight loss = 4 pounds In the eighth week, 4 pounds need to be lost in order to meet the weight loss goal of 15 pounds in 8 weeks.