Answer :
Final answer:
To determine Mr. Riley's starting weight for his weight loss program, we calculated the time both individuals reached their goal and the coinciding weight loss each per week. Mr. Riley started at 222 pounds and reached the goal of 180 pounds in 7 weeks by losing 6 pounds per week.
Explanation:
Mr. Riley and Mr. Smith are both aiming to reach a weight of 180 pounds by losing weight at different rates weekly. Mr. Riley's goal is to lose 6 pounds a week, while Mr. Smith intends to lose 3 pounds a week, starting two weeks after Mr. Riley. They both achieved their slow and steady weight-loss goals and reached 180 pounds at the same time.
Let's calculate the weight at which Mr. Riley started his diet and exercise program.
Since Mr. Smith lost 3 pounds per week and started two weeks after Mr. Riley, we know that he must have lost weight for the same number of weeks as Mr. Riley minus two weeks. We also know that Mr. Smith started at 195 pounds, and when he reached 180 pounds, he must have lost a total of 195 - 180 = 15 pounds.
This means Mr. Smith was losing weight for 15 pounds / 3 pounds per week = 5 weeks.
Since Mr. Riley's weight loss overlapped with Mr. Smith's for these 5 weeks but also included the additional 2 weeks before Mr. Smith started, Mr. Riley was losing weight for a total of 5 weeks + 2 weeks = 7 weeks.
At 6 pounds per week, Mr. Riley would have lost a total of 7 weeks * 6 pounds per week = 42 pounds.
Therefore, to find out Mr. Riley's starting weight, we take the weight he ended at, which was 180 pounds, and add the weight he lost, which was 42 pounds. So, Mr. Riley started at 180 pounds + 42 pounds = 222 pounds.
