A cart carries 100 pounds of cucumbers. The cucumbers are 95% water, and during the day they lose water rapidly on a hot, dry day. After a day passes by, the cucumbers are now 90% water. How much much do the cucumbers weigh after drying out?
To find out how much the cucumbers weigh after drying out, we need to determine the amount of water lost during the day.
Let's start by calculating the initial weight of water in the cucumbers. The cucumbers are 95% water, so we can calculate it as follows:
Initial weight of water = 0.95 * 100 pounds = 95 pounds
Now, let's calculate the weight of the cucumbers after drying out. The cucumbers are now 90% water, so the remaining weight is the dry weight of the cucumbers, which we'll call x:
90% of (100 pounds - x) = x
To solve this equation, we first convert 90% to a decimal by dividing it by 100, which gives us 0.90:
0.90 * (100 pounds - x) = x
Distributing the 0.90, we get:
90 pounds - 0.90x = x
Now, let's solve for x:
90 pounds = 1.90x
Dividing both sides by 1.90, we get:
x = 90 pounds / 1.90 = 47.37 pounds (rounded to two decimal places)
Therefore, the cucumbers weigh approximately 47.37 pounds after drying out.