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At present, Mark's age is x^2 years and Peter's age is x years. When mark is 10x years, Peter will be 3x years. What are their present ages?
Question is kind of confusing to me, so again i just need help forming the equation. Thanks.
Mark now is x^2
at some time in the future, Mark is 10x
so the change in time is 10x - x^2
Peter's age will change by that same number
so Peter's age will be x + 10x-x^2
= 11x - x^2
but 3x = 11x- x^2
x^2 - 8x = 0
x(x-8) = 0
x = 0 , not likely
or
x = 8
So Mark is now 64 and Peter is now 8
check:
When Mark is 80, sixteen years from now, Peter will be 16+8 or 24 years, which is 3(8)
All is good.
Well, it seems like Mark's age is given by x^2 years and Peter's age is x years. We also know that when Mark is 10x years old, Peter will be 3x years old. To find their present ages, we can set up the equation like this:
x^2 = Mark's present age
x = Peter's present age
Now, let's consider the future scenario when Mark is 10x years old and Peter is 3x years old. We'll set up the equation based on the information given:
10x = Mark's future age
3x = Peter's future age
It's important to remember that in the future, when Mark is 10x years old, Peter will also need to be 3x years old.
So, now we have the equations:
10x = 3x
To solve for x, we can divide both sides of the equation by 3:
10x/3 = 3x/3
10/3 * x = 1x
10/3 = x
So, we've found that x = 10/3.
Now we can substitute this value back into the initial equations to find their present ages:
Mark's present age = x^2 = (10/3)^2 = 100/9
Peter's present age = x = 10/3
Therefore, Mark's present age is 100/9 years and Peter's present age is 10/3 years. But keep in mind that this is a bit of a mathematical clowning around!
To solve this problem, we can create two equations based on the given information and then solve them simultaneously.
Let's denote Mark's present age as M and Peter's present age as P.
According to the information given:
1) Mark's age at present is x^2 years: M = x^2
2) Peter's age at present is x years: P = x
We also know that when Mark is 10x years, Peter will be 3x years older than his present age:
3) M + 10x = P + 3x
Now we have a system of two equations:
M = x^2 (Equation 1)
M + 10x = P + 3x (Equation 2)
By substituting the value of P from Equation 2 into Equation 1, we can solve for M:
x^2 + 10x = x + 3x
x^2 + 10x - x - 3x = 0
x^2 + 6x = 0
x(x + 6) = 0
So either x = 0 or x + 6 = 0.
Since the age of a person cannot be zero, we can conclude that x + 6 = 0.
Solving for x, we have:
x = -6
Substituting this value of x back into the equations:
M = (-6)^2 = 36
P = -6
Therefore, Mark's present age is 36 years and Peter's present age is -6 years.
To solve this problem, let's break it down step by step:
1. Let's first assign variables to Mark's and Peter's current ages. Let Mark's current age be m and Peter's current age be p.
2. According to the information given, Mark's age is x^2 years, so we can write this as m = x^2.
3. Peter's age is given as x years, so we can write this as p = x.
4. The problem also states that when Mark is 10x years old in the future, Peter will be 3x years old. Let's calculate the future ages:
Mark's future age = m + 10x
Peter's future age = p + 10x
Therefore, Mark's future age = x^2 + 10x
And Peter's future age = x + 10x
5. Based on the information given, we can set up an equation: Mark's future age (x^2 + 10x) = 3 times Peter's future age (x + 10x). This can be written as:
x^2 + 10x = 3(x + 10x)
6. Now we can simplify and solve the equation:
x^2 + 10x = 3x + 30x
x^2 + 10x = 33x
x^2 = 23x
7. Divide both sides of the equation by x:
x^2 / x = 23x / x
x = 23
8. Now we know that x = 23. Substitute this value back into the original equations:
Mark's current age (m) = x^2 = 23^2 = 529 years
Peter's current age (p) = x = 23 years
Therefore, Mark's present age is 529 years, and Peter's present age is 23 years.