Jennifer is 6 years older than Sue. In 4 years, she will be twice as old as Sue was 5 years ago. Find there ages now
Let's represent Jennifer's current age as J and Sue's current age as S.
According to the information given, Jennifer is 6 years older than Sue:
J = S + 6 (Equation 1)
In 4 years, Jennifer will be J + 4 years old, and Sue will be S + 4 years old.
It is also mentioned that in 4 years, Jennifer will be twice as old as Sue was 5 years ago:
J + 4 = 2(S - 5) (Equation 2)
Now we can solve this system of equations to find their current ages.
Substituting the value of J from Equation 1 into Equation 2, we get:
S + 6 + 4 = 2(S - 5)
S + 10 = 2S - 10
10 + 10 = 2S - S
20 = S
Therefore, Sue is currently 20 years old.
Substituting this value back into Equation 1, we can find Jennifer's current age:
J = S + 6
J = 20 + 6
J = 26
Therefore, Jennifer is currently 26 years old.
Hence, Jennifer is 26 years old and Sue is 20 years old.
To solve this problem, let's break it down step by step and set up equations to represent the given information.
Let's assume that Sue's current age is "x" years. Therefore, Jennifer's current age would be "x + 6" since she is 6 years older than Sue.
According to the problem, in 4 years, Jennifer will be twice as old as Sue was 5 years ago. So, we can set up the following equation:
(x + 6) + 4 = 2(x - 5)
Let's solve this equation to find the value of x, which represents Sue's current age:
x + 10 = 2x - 10
By bringing the "x" terms to one side and the constant terms to the other side, we get:
x - 2x = -10 - 10
Simplifying the equation further, we have:
-x = -20
Now, by multiplying both sides of the equation by -1 to isolate "x," we get:
x = 20
Therefore, Sue's current age is 20 years old. Since Jennifer is 6 years older, her current age is:
x + 6 = 20 + 6 = 26
Hence, Sue is currently 20 years old, and Jennifer is currently 26 years old.