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.
math 7 accelerated - tom, Tuesday, September 24, 2013 at 6:46pm
Ms. Sue thanks for the help. I really appreciate it
To solve this problem, we need to set up a system of equations based on the given information.
Let's use the variables Y, T, and H to represent the ages of Yanira, Tim, and Hannah, respectively.
From the information given, we can set up the following equations:
Equation 1: Y = T + 3 (Yanira is 3 years older than Tim)
Equation 2: Y = 2H (Yanira is twice as old as Hannah)
Equation 3: T = H + 2 (Tim is 2 years older than Hannah)
Now, let's substitute the values from Equation 3 into Equation 1:
Y = (H + 2) + 3
Y = H + 5
Substituting this new value of Y into Equation 2:
H + 5 = 2H
Simplifying this equation:
H = 5
Now, substituting this value of H into Equation 3:
T = 5 + 2
T = 7
Finally, substituting the values of T and H into Equation 1:
Y = 7 + 3
Y = 10
Therefore, Yanira is 10 years old, Tim is 7 years old, and Hannah is 5 years old.
The answer is: Yanira is 10 years old, Tim is 7 years old, and Hannah is 5 years old.
y = t+3
y = 2h
t = h+2
sub top and bottom into middle:
t+3 = 2(t-2)
t+3 = 2t-4
t = 7
so, y=10 and h=5