Answer:
The amount each took home was 20 unit currency.
Step-by-step 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.
