Answer:
a) my age is 36, sister's age is 24 b) my age is 48, the sister's age is 36
c) my age is 96, sister's age is 84 Extension: 21.7percents
Explanation:
Suppose now I am x , my sister is y (x years, y years)
Six years ago I was x-6, my sister was y-6, I was 7 times older than my sister
x-6= (y-6)*7
x-6=7y-42
x-7y=-36
Four years ago I was x-4, my sister was y-4. I was 4 times older.
x-4= (y-4)*4
x-4=4y-16
x-4y=-12
We have the system of equations
x-7y=-36
x-4y=-12
4y-x=12
x-7y+4y-x=-36+12
-3y=-24
y=8
x-32=-12
x=20
The difference between us is 20-8=12. It is constant measure.
So if my sister is m, I am m+12
a) (m+12)*2/3=m
2/3m+8=m
1/3m=8
m=24- the age of my sister
24+12=36- my age
b) 3/4*(m+12)= m
3/4m+9=m
m=36- her age
36+12=48- my age
c) 7/8(m+12)= m
1/8m= 84/8
m=84- her age
84+12=96- my age
Extension
6/1/7=42- the age of Ian when Jamie will be six
10-6=4- years (after four years Jamie will be 10)
42+4=46- the age of Ian after 4 years
46-100
10-x
x= 100/4.6= 21.7percents is an approximate percentage which Jamie's age is from Ian