Jeff weighed 190 pounds and lost 1/4 pound each week. Allan weighed 127 pounds and gained 5/8 pound each week. After how many weeks did they weigh the same?

Question

Jeff weighed 190 pounds and lost 1/4 pound each week. Allan weighed 127 pounds and gained 5/8 pound each week. After how many weeks did they weigh the same?

Answer 1

190 - W/4 = 127 + 5W/8

subtract 127 from both sides

add W/4 to both sides to get

63 = ((5/8+1/4)W

(7/8) W = 63

W = (8/7)63 = 8x9 = 72 weeks or about 1 1/2 years

in 72weeks, Jeff loses 72/4 =18 lbs, and goes from 190 to 172 lbs.

in 168 weeks, Allan gains 72(5/8) = 9x5=105 going from 127 to 172 lbs.

Answer: 72 weeks

52 weeks in a year, so it's one year + 20 weeks