There was a total of 18 apples
<u>Step-by-step explanation:</u>
Let us consider the total no. of apples be 'a'.
Patriarca took 1/6 of the apples. So the remaining apples is,
a - (1/6) a= (5/6) a
Step 1:
His wife takes (1/5) of the rest of the apples. So after she takes the apples the remaining apples will be,
(5/6) a - (1/5) (5/6) a
(5/6) a - (1/6) a = (4/6) a
Step 2 :
Her elder son takes (1/4) of the remaining apples. So,
(4/6) a - (1/4) (4/6) a
(4/6) a - (1/6) a = (3/6) a
Step 3:
Middle son takes (1/3) of the remaining apples. So,
(3/6) a - (1/3) (3/6) a
(3/6) a - (1/6) a = (2/6) a
Step 4:
Younger son takes (1/2) of the remaining apples. So,
(2/6) a - (1/2) (2/6) a
(2/6) a - (1/6) a = (1/6) a
After work she takes the remaining 3 apples. So the remaining apples were 3
So,
(1/6) a = 3
a = 3 x 6
a = 18 apples
There were a total of 18 apples.
