Frank is 5 years older than Mary. In 5 years, Frank will be twice as old as Mary is now. How old is Mary now?
f = m+5
f+5 = 2m
m+5 + 5 = 2m
m = 5
Mary is currently 10.
Frank is 15.
In 5 years he'll be 20 which is twice as much/old as Mary's current 10.
F = M + 5 and M2 = F + 5
F - M = 5 and M2 - F = 5
(F - F) + (2M - M) = 10
M = 10
To solve this problem, let's break it down step by step:
1. Let's assume Mary's age is "x" years.
2. According to the given information, Frank is 5 years older than Mary. Therefore, Frank's age would be "x + 5" years.
3. In 5 years, Frank's age will be "x + 5 + 5" years, which simplifies to "x + 10" years.
4. At the same time, Mary's age in 5 years will be "x + 5" years since she does not age 5 years twice.
5. According to the problem, Frank will be twice as old as Mary is now in 5 years. So we can set up the equation: "x + 10 = 2(x + 5)."
6. Let's solve the equation:
x + 10 = 2x + 10
- x - 10 = 2x + 10 - 10 (subtracting x and 10 from both sides)
- x - 10 = 2x
-10 = 2x + x (combining like terms)
-10 = 3x
x = -10 / 3 (dividing both sides by 3)
x = -3.33 (rounded to two decimal places)
Since age cannot be negative in this context, it is not a reasonable solution. So, we can conclude that there is no valid solution to this problem based on the given information.