Two contestants on the show The Biggest Loser start out weighing the same. At the end of year one, contestant A had lost 10% of his weight while contestant B gained 10% of his starting weight. At the end fo year two, contestant A had gained back 10% of his end-of-year-one weight while contestand B lost 10% of his end-of-year-one weight. Who was slimmer at the end of year two?
Please do not switch names -- as you've done for the last seven posts.
They both weigh the same
To determine who was slimmer at the end of year two, we need to compare the weights of contestant A and contestant B. Let's break down the information step by step.
1. Start by assigning a specific weight to both contestants. Since they start out weighing the same, let's assume that their initial weight is 100 units (you can choose any value as long as it is consistent).
2. At the end of year one, contestant A lost 10% of his weight. To calculate his weight at the end of year one, subtract 10% (0.10) of his starting weight from his initial weight: 100 - (100 * 0.10) = 100 - 10 = 90 units.
3. At the end of year one, contestant B gained 10% of his starting weight. To calculate his weight at the end of year one, add 10% (0.10) of his starting weight to his initial weight: 100 + (100 * 0.10) = 100 + 10 = 110 units.
4. At the end of year two, contestant A gained back 10% of his weight from the end of year one. To calculate his weight at the end of year two, add 10% (0.10) of his year-one weight to his year-one weight: 90 + (90 * 0.10) = 90 + 9 = 99 units.
5. At the end of year two, contestant B lost 10% of his weight from the end of year one. To calculate his weight at the end of year two, subtract 10% (0.10) of his year-one weight from his year-one weight: 110 - (110 * 0.10) = 110 - 11 = 99 units.
Comparing the weights at the end of year two, we can see that both contestant A and contestant B weigh 99 units, which means they are equal in weight. Therefore, neither contestant is slimmer than the other at the end of year two.