Question

susan is 4 years older than her sister rita. Seven years ago, Susan was twice as old as Rita. How old are they now?

Answer 1

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