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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?

User Alessmar
by
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1 Answer

1 vote

Answer:

The amount each took home was 20 unit currency.

Explanation:

The given parameters are

The number of apples with each of the seven apple women = 20, 40, 80, 100, 120, and 140

The number of apples each woman has can be written in the following formula obtained online which is a series formula

a·n + (n - 1), (a + b)·n + (n - 2), (a + 2·b)·n + (n - 3), (a + 3·b)·n + (n - 4), (a + 4·b)·n + (n - 5), (a + 5·b)·n + (n - 6), (a + 6·b)·n + (n - 7)

Which gives;

a·n + (n - 1) = 20

(a + b)·n + (n - 2)=40

(a + 2·b)·n + (n - 3) = 60

(a + 3·b)·n + (n - 4) = 80

(a + 4·b)·n + (n - 5) = 100

(a + 5·b)·n + (n - 6) = 120

(a + 6·b)·n + (n - 7) = 140

Solving the above system, we get

n = 7, a = 2, b = 3

Which gives

2×7 + 6 = 20

5×7 + 5=40

8×7 + 4 = 60

11×7 + 3 = 80

14×7 + 2 = 100

17×7 + 1 = 120

20×7 + 0 = 140

Whereby all the women sold the apples for the same sum price, based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount taking home by each of them given as follows;

2×1 + 6×3 = 20

5×1 + 5×3=20

8×1 + 4×3 = 20

11×1 + 3×3 = 20

14×1 + 2×3 = 20

17×1 + 1×3 = 20

20×1 = 20

Therefore, the amount each took home was 20 unit currency.

User Iefserge
by
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