Yanira is 3 years older than Tim and twice as old as Hannah. Tim is 2 years older than Hannah. How old are Yanira Tim and Hannah?
Explain how you did the problem and the answer.
Tim's age --- x
Yanira's age -- x+3
Hannah's age = (1/2)(x+3)
Tim is 2yrs older than Hannah
----> x = (1/2)(x+3) + 2
times 2
2x = x+3 + 4
x = 7
So Tim is 7
Yanira is 10
Hannah is 5
All conditions are met.
To solve this problem, we need to use the given information and create a system of equations.
Let's denote Yanira's age as Y, Tim's age as T, and Hannah's age as H.
Based on the information given, we can create the following equations:
1. Yanira is 3 years older than Tim:
Y = T + 3
2. Yanira is twice as old as Hannah:
Y = 2H
3. Tim is 2 years older than Hannah:
T = H + 2
Now we can solve this system of equations.
Substituting equation (2) into equation (1) gives us:
2H = T + 3
Substituting equation (3) into the previous equation gives us:
2H = H + 2 + 3
2H = H + 5
H = 5
Now that we know the age of Hannah is 5, we can substitute this value into equation (3) to find Tim's age:
T = 5 + 2
T = 7
Finally, substituting the values of Tim and Hannah into equation (2), we can find Yanira's age:
Y = 2(5)
Y = 10
So the final answer is:
Yanira is 10 years old,
Tim is 7 years old, and
Hannah is 5 years old.