susan is 4 years older than her sister rita. Seven years ago, Susan was twice as old as Rita. How old are they now?
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
To find out the current ages of Susan and Rita, we can solve the problem using algebraic equations.
Let's assume Rita's current age is "r" years. According to the problem, Susan is 4 years older, so her current age would be "r + 4" years.
Now, seven years ago, Rita's age would have been "r - 7" years, and Susan's age would have been "r + 4 - 7" years.
According to the problem, Susan was twice as old as Rita seven years ago, so we can set up the following equation:
(r + 4 - 7) = 2 * (r - 7)
Let's solve the equation step by step:
r - 3 = 2r - 14 (Distributing the 2 on the right side)
r - 2r = -14 + 3 (Subtracting r from both sides)
-r = -11 (Simplifying)
r = 11 (Multiplying both sides by -1 and changing the sign)
r + 4 = 11 + 4 = 15
Therefore, Rita is currently 11 years old, and Susan is 15 years old.