Fiona and camila took a load of peaches to the farmers market. During the first hour , they sold 1/2 of the peaches plus 1/2 of a peach. In the second hour, they sold 1/3 of the remaining peaches plus 1/3 of a peach. In the third hour , they sold 1/4 of what was left and 3/4 of a peach. During the final hour, they sold 1/5 of the peaches that were left plus 1/5 of a peach. Fiona and camila did not cut any peaches to make a sale, and they returned home with 19 whole peaches. How many peaches did they take to the market?
This is a ridiculous problem. No one could sell a fraction of a peach!
To solve this problem, we will work backward from the final hour where Fiona and Camila returned home with 19 whole peaches.
Let's denote the total number of peaches originally taken to the market as "P".
During the final hour, they sold 1/5 of the remaining peaches plus 1/5 of a peach. So, the number of peaches remaining after the third hour would be 5 times the number of peaches they brought back home (19).
Number of peaches remaining after the third hour = 5 * 19 = 95
In the third hour, they sold 1/4 of what was left and 3/4 of a peach. So, the number of peaches remaining after the second hour would be 4 times the number of peaches after the third hour (95).
Number of peaches remaining after the second hour = 4 * 95 = 380
In the second hour, they sold 1/3 of the remaining peaches plus 1/3 of a peach. So, the number of peaches remaining after the first hour would be 3 times the number of peaches after the second hour (380).
Number of peaches remaining after the first hour = 3 * 380 = 1140
In the first hour, they sold 1/2 of the peaches plus 1/2 of a peach. So, the number of peaches originally taken to the market (P) would be 2 times the number of peaches after the first hour (1140).
P = 2 * 1140 = 2280
Therefore, they originally took 2280 peaches to the market.