124. How Many Apples Were Picked at the First Tree?
Three friends went apple picking and collected a total of 65 apples.
• At the first tree each person picked the same number of apples.
• At the second tree each person picked three times as many apples as they had picked at the first tree.
• When they finished picking from the third tree, the group had five times as many apples as they had when they started at that tree.
• At the fourth and final tree the group picked exactly 5 more apples.
Altogether the three friends now had 65 apples. How many apples did each person pick at the first tree?
Added 22 September 2012
Hint: Let x be the number of apples each person picked at the first tree. Translate each bullet into an equation, keeping track of the running total.
Solution:
Let x be the number of apples each friend picked at the first tree.
First tree: total = 3x.
Second tree: each picks 3x more, so total second-tree harvest = 3 × 3x = 9x.
Cumulative total after second tree = 3x + 9x = 12x.
Third tree: when they finish, they have 5 times what they had when they started this tree, i.e. 5 × 12x = 60x.
They therefore picked 60x − 12x = 48x at the third tree.
Fourth tree: they add 5 apples, giving a final total of 60x + 5.
This final total is given as 65 apples, so
60x + 5 = 65 ⇒ 60x = 60 ⇒ x = 1.
Therefore each person picked 1 apple at the first tree.
Comments (1)
1 each.
Giving three apples total, followed by picking three times that many at tree 2 to make twelve, five times 12 is 60 after tree 3, 60+ "group" 5 = 65.
Add a Comment or Suggest an Answer