Fresh Grapes contain 80 percent water by weight and 20 percent juice, whereas dried grapes contain 15 percent water by weight with the rest juice. How many punds of dried grapes are needed to yield the same amount of juice as 34 pounds of fresh grapes?
34lbs*(.2)=6.8lbs of juice from the fresh grapes.
let x=# of pounds of dried grapes needed
We know dried grapes are 85 percent juice (.85). We also know we want 6.8lbs of juice.
.85x=6.8
solve for x
To find out how many pounds of dried grapes are needed to yield the same amount of juice as 34 pounds of fresh grapes, we need to determine the amount of juice in both fresh and dried grapes.
Let's start by finding the amount of juice in 34 pounds of fresh grapes. Since fresh grapes contain 20 percent juice, we can calculate the weight of the juice as follows:
Weight of juice in fresh grapes = 20% of 34 pounds
= (20/100) * 34
= 0.2 * 34
= 6.8 pounds
Next, we need to determine the weight of dried grapes required to yield the same amount of juice. Since dried grapes contain 15 percent water and the remaining percentage is juice, we can calculate the weight of dried grapes as follows:
Weight of dried grapes = Weight of juice / Percentage of juice in dried grapes
= 6.8 pounds / 15%
= 6.8 pounds / (15/100)
= 6.8 pounds / 0.15
= 45.33 pounds
Therefore, approximately 45.33 pounds of dried grapes are needed to yield the same amount of juice as 34 pounds of fresh grapes.