Question

Sandra and Bernice are starting a nutrition and exercise program that will last 12 weeks. Sandra is starting at 150 pounds and plans to lose 1 pound a week. Bernice is starting at 135 pounds and plans to lose 1/2 a pound a week. When during the program will Bernice and Sandra weigh the same?

Answer 1

They will not have the same weight during the program

Explanation:

Let x be the number of weeks.

Sandra:

Sandra is starting at 150 pounds and plans to lose 1 pound a week.

Weight after x weeks:

`150-x`

Bernice:

Bernice is starting at 135 pounds and plans to lose 1/2 a pound a week.

Weight after x weeks:

`135-(1)/(2)x`

Weights must be the same, so

`150-x=135-(1)/(2)x\\ \\(1)/(2)x-x=135-150\\ \\-(1)/(2)x=-15\\ \\x=30`

Since 30 weeks is more that 12 weeks (the duration of the program), they will not have the same weight during this program.