Nancy is 6 times as old as Mary. When will she be only twice as old as Mary?
In x years, we will have
6m+x = 2(m+x)
6m+x = 2m+2x
4m = x
So, no matter what Mary's age is now, in 4 times that many years Nancy will only be twice as old.
For example, if Mary is now 5,
Mary is 5 and Nancy is 30
In 20 years, Mary will be 25 and Nancy will be 50.
Let's assume Mary's current age is represented by "x". According to the given information, Nancy is 6 times as old as Mary, so Nancy's current age can be represented as 6x.
We need to find the point in time when Nancy will be twice as old as Mary. Let's say "t" represents the number of years from now.
In "t" years from now, Mary's age will be x + t, and Nancy's age will be 6x + t.
According to the problem, Nancy will be twice as old as Mary at that point, so we can create the equation:
6x + t = 2 * (x + t)
Now let's solve this equation step by step.
Expanding the right side of the equation:
6x + t = 2x + 2t
Moving all the "x" terms to one side and all the "t" terms to the other side:
6x - 2x = 2t - t
Simplifying:
4x = t
Thus, according to the equation, in "t" years from now, Mary's age will be equal to Nancy's age.
Therefore, Nancy will be only twice as old as Mary in "t" years.
To solve this problem, we need to set up an equation based on the given information. Let's suppose Nancy's current age is represented by "N" and Mary's current age is represented by "M".
According to the problem, Nancy is 6 times as old as Mary, which can be written as:
N = 6M
We are asked to find out when Nancy will be only twice as old as Mary. Let's assume the number of years from now when Nancy will be twice as old as Mary is represented by "x".
So, after "x" years, Nancy's age will be N + x, and Mary's age will be M + x.
According to the problem, Nancy will be twice as old as Mary after "x" years, which can be written as:
N + x = 2(M + x)
Now, we have two equations:
N = 6M ---(equation 1)
N + x = 2(M + x) ---(equation 2)
To solve these equations simultaneously, substitute the value of N from equation 1 into equation 2:
6M + x = 2(M + x)
Next, distribute the 2 to M and x:
6M + x = 2M + 2x
Combining like terms:
6M - 2M = 2x - x
4M = x
So, x = 4M.
This means that after 4 years, Nancy will be twice as old as Mary.