Fiona and Camilla took a load of peaches to the farmer’s market.
- During the first hour, they sold \(\frac{1}{2}\) of the peaches plus \(\frac{1}{2}\) of a peach.
- In the second hour, they sold \(\frac{1}{3}\) of the remaining peaches plus \(\frac{1}{3}\) of a peach.
- In the third hour, they sold \(\frac{1}{4}\) of what was left plus \(\frac{3}{4}\) of a peach.
- During the final hour, they sold \(\frac{1}{5}\) of the peaches that were left plus \(\frac{1}{5}\) of a peach.
Fiona and Camilla went home with 19 whole peaches. How many peaches did they take to the market?
Answer (2)
They took 101 peaches to market.
Check:
In the 1st hour, they sold (101/2 + 1/2) = 102/2 = 51. They had 50 left.
In the 2nd hour, they sold (50/3 + 1/3)=51/3=17. They had (50-17)=33 left.
In the 3rd hour, they sold (33/4 + 3/4) = 36/4 = 9. They had (33-9) = 24 left.
In the final hour, they sold (24/5 + 1/5) = 25/5 = 5. They had (24-5) = 19 left. yay!
Fiona and Camilla took their 19 remaining peaches and went home. Sharing with their parents and their brother Rowlf, each person had 3.8 peaches for dinner. There was a lot of activity in the bathroom overnight.
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The key to solving this one is to work it backwards.
-- They had 19 peaches left at the end of the day.
-- During the final hour, the 1/5 of a peach that they sold left them with 19, so they had 19-1/5 before they sold the 1/5 of a peach. The 19-1/5 was 4/5 of what they had at the beginning of the final hour. So, at the beginning of the final hour, they had (5/4)x(19.2) = 24 .
-- During the 3rd hour, the 3/4 of a peach that they sold left them with 24, so they had 24-3/4 before they sold the 3/4 of a peach. The 24-3/4 was 3/4 of what they had at the beginning of that hour. So, at the beginning of the 3rd hour, they had (4/3)x(24.75) = 33 .
Do the same for the 2nd hour.
Then do the same for the 1st hour.
And you'll work your way back up to 101 peaches.
Fiona and Camilla initially took 101 peaches to the market. By working backwards through each hour of sales, starting from the 19 peaches left, we can clearly see how many peaches they sold and how many were remaining at each step. This calculation helps us determine that their starting number of peaches was indeed 101.
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