Question

THE SEVEN APPLEWOMEN

Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
apples, went to market and sold all their apples at the same price, and each
received the same sum of money. What was the price?

Answer 1

• Price was 1 unit of money per each 7 apples and 3 units of money per each extra apple
• Each woman received 20 unit of money

Explanation:

This is the tricky one

I think 'The Seven Apple' is the hint. Let's see what the numbers have to do with 7:

• 20 = 7*2 + 6
• 40 = 7*5 + 5
• 60 = 7*8 + 4
• 80 = 7*11 + 3
• 100 = 7*14 + 2
• 120 = 7*17 + 1
• 140 = 7*20 + 0

Assume each '7 apples' sold for a fixed price x and each 'extra' apple sold for a different price y. Since all add up to make same amount, we get:

• 2x + 6y = 5x + 5y = ... = 20x

Let x = 1, then we get y = 3

So we get the sold price:

• 20 apples cost: 2*1 + 6*3 = 20
• 40 apples cost: 5*1 + 5*3 = 20
• ...
• 140 apples cost: 20*1 = 20

So each apple woman got 20 units of money for their apples.

Price was 1 unit of money per each 7 and 3 units of money per each extra apple

Answer 2

zero

Explanation:

If the same sum is received for the sale of 20 apples at price p as is received for the sale of 140 apples at price p, then we must have ...

20p = 140p

120p = 0 . . . . . . subtract 20p

p = 0 . . . . . . . . . divide by 120

The price was zero.