S = Susan's age
R = Ritas's age
Susan is 4 years older than her sister Rita.
This mean :
S = R + 4
Seven years ago Susan was ( S - 7 ) yrs old, and Rita was ( R - 7 ) yrs old.
Seven years ago, Susan was twice as old as Rita.
This mean :
( S - 7 ) / ( R - 7 ) = 2
Replace S with R + 4 in this equation.
( R + 4 - 7 ) / ( R - 7 ) = 2
( R - 3 ) / ( R - 7 ) = 2 Multiply both sides by ( R - 7 )
R - 3 = 2 ( R - 7 )
R - 3 = 2 * R - 2 * 7
R - 3 = 2 R - 14 Subtract R to both sides
R - 3 - R = 2 R - 14 - R
- 3 = R - 14 Add 14 to both sides
- 3 + 14 = R - 14 + 14
11 = R
R = 11 yrs old
S = R + 4 = 11 + 4 = 15 yrs old
Susan's age = 15
Rita's age = 11
Proof:
Seven years before Susan was 15 - 7 = 8 yrs old , and Rita was 11 - 7 = 4 yrs old
8 / 4 = 2
susan is 4 years older than her sister rita. Seven years ago, Susan was twice as old as Rita. How old are they now?
1 answer