### Brain Teasers

# Apple Picking

Three people picked 65 apples altogether. At the first tree they each picked the same number of apples. At the second tree they each picked 3 times as many as they picked at the first tree. When they finished at the third tree, the group had 5 times as many apples as they had when they started at that tree. At the fourth tree the group picked just 5 apples.

How many apples did each person pick at the first tree?

How many apples did each person pick at the first tree?

### Hint

Work backwards to see how many apples were picked at the last two trees or use algebra.### Answer

Each person picked 1 apple at the first tree.Begin with 65 apples picked, and work backwards. Subtract the number of apples picked at the fourth tree (5), and then divide the total (60) by 5 to equal the number of apples picked after the first two trees. The total after the first two trees = 12. Since the number of apples picked at the first two trees (12) is equal to the number of apples picked at the first tree plus 3 times the number picked at the first tree (or a total of 4 times the number picked at the first tree), then the number of apples picked at the first tree must be 12 divided by 4 = 3. Therefore, each person picked 1 apple at the first tree.

Using algebra: Suppose they pick y apples at the first tree. Then, they pick 3y apples at the second tree and have 4y apples altogether. After the third tree, they have 5X4y or 20y apples, and after the fourth tree, they have 20y + 5 apples.

20y + 5 = 65

20y = 60

y = 3

So each person picks 1 apple at the first tree.

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