Steve is 3 years older than Tim and twice as old as Hannah. Tim is 2 years older than Hannah. How old are Steve,Tim and Hannah?
s = t+3
s = 2h
t = h+2
so, let's solve for Hannah.
t = h+2
t+3 = 2h, so t = 2h-3
That gives us
h+2 = 2h-3
h = 5
So, Hannah is 5, Tim is 7, Steve is 10 (which is twice as old as Hannah)
To find the ages of Steve, Tim, and Hannah, we can break the problem down into steps:
Step 1: Define the variables.
Let's say:
- Steve's age is S,
- Tim's age is T,
- Hannah's age is H.
Step 2: Translate the given information into equations.
From the problem statement, we can write the following equations:
1. Steve is 3 years older than Tim: S = T + 3.
2. Steve is twice as old as Hannah: S = 2H.
3. Tim is 2 years older than Hannah: T = H + 2.
Step 3: Solve the equations to find the ages.
We will use substitution to solve the system of equations.
Substitute equation 2 into equation 1:
2H = T + 3.
Substitute equation 3 into the updated equation 1:
2H = (H + 2) + 3,
2H = H + 5,
H = 5.
Substitute H = 5 into equation 3 to find Tim's age:
T = 5 + 2,
T = 7.
Substitute H = 5 into equation 2 to find Steve's age:
S = 2 * 5,
S = 10.
Therefore, Steve is 10 years old, Tim is 7 years old, and Hannah is 5 years old.