Congratulations to Nathan Lee (physics student) for coming up with the solution to the first challenge problem. The problem was as follows:
Assume you are a truck driver delivering California strawberries to the Cedarville area. When you leave southern California, you have the back of your truck filled with 10 tons of strawberries. You check the water content of these berries and find them to be 95% water. While driving across the hot highway your berries dry out a little. (You should have had a refrigerator truck!) By the time you get to Cedarville the berries are 90% water. What is the weight of your strawberries when you deliver them to Cedarville?
Since the percentage of water drops from 95% to 90%, it appears that the humidity problem in your truck isn’t that bad. However, by the time you get back to Cedarville you find that your 10 tons of strawberries has become 5 tons.
Whenever you work with percentages, you have to be careful about what is changing and what is not. In this case the water content is changing, but the solid portion of the strawberry remains constant. When you begin in California, you have 95% water which translates into 9.5 tons of water and 5% solid strawberry which translates into 0.5 tons. At Cedarville you still have 0.5 tons of solid strawberry, but the percentage of water has dropped to 90%. Let’s say that the amount of water in the strawberries at Cedarville is W. Then the total weight of the strawberries would be W + 0.5. 90% of this total weight has to be water; therefore, we get the equation 90%(W + 0.5) = W.
Solving for W gives W = 0.90*0.5/(1-.90) = 4.5. The amount of water is then 4.5 tons and the solid strawberry weight is 0.5 tons giving a total weight of 5.0 tons.
Posted in: Challenge Problem