SOLUTION: Yaniara is 3 years older than Tim and she is twice as old as Hannah. Tim is 2 years older than Hannah. How old are Yanaira, Tim and Hannah? I believe X = Tim's age X+3 = Y

Question 1049121: Yaniara is 3 years older than Tim and she is twice as old as Hannah. Tim is 2 years older than Hannah. How old are Yanaira, Tim and Hannah?
I believe
X = Tim's age
X+3 = Yaniars age
X-2 = Hannah
Trying to help my daughter with homework problem. I am sorry I am not good with these
Found 4 solutions by josmiceli, josgarithmetic, ikleyn, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
This is the way I do it:
Let = Tim's age
Let = Yaniara's age
Let = Hannah's age
---------------------------
(1)
(2)
(3)
--------------------
Substitute (2) into (1)
(1)
(1)
and
(3)
--------------------
Now add (1) and (3)
(1)
(3)
--------------------

and
(2)
(2)
(2)
and
(3)
(3)
(3)
--------------------
Tim is 7
Yaniara is 10
Hannah is 5
---------------
check answers:
Yaniara is 3 years older than Tim
YES
she is twice as old as Hannah.
YES
Tim is 2 years older than Hannah.
YES

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Yaniara is 3 years older than Tim and she is twice as old as Hannah. Tim is 2 years older than Hannah.

x, variable for Tim's age, using small letter instead of capital letter (arbitrary but needs to be consistent.)

Yaniara,

No variable was assigned to Hannah, but you chose none for Hannah.
Yaniara is twice as old as Hannah: . You need a variable for Hannah's age; and here, I chose h.

Tim is two years older than Hannah: .

--
Do you follow that? There are now two equations using two unknown variables of x and h.

A more organized way to analyze and arrange the equations:
Assign a variable each to the different people.

t, Tim y, Yaniara h, Hannah

Not as bad as it may first appear.

Now go through the description again and literally translate into symbols.

-
See that you know what each unknown variable stands for; you just do not know how much yet.

That analysis and arranging equations was the "hard" part.
Your daughter most likely can solve the system for each of the variables.
She might see that there are two formulas for y, and their expressions can be equated, so this would give a system equivalent to:

Simple substitution will allow for a solved value for h.
She should be able to handle the remaining two variables.
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.
Yaniara is 3 years older than Tim and she is twice as old as Hannah. Tim is 2 years older than Hannah. How old are Yanaira, Tim and Hannah?
I believe
X = Tim's age
X+3 = Yaniars age
X-2 = Hannah
Trying to help my daughter with homework problem. I am sorry I am not good with these
~~~~~~~~~~~~~~~~~~~~~~~~

Y = T + 3, (1) ("Yaniara is 3 years older than Tim ") Y = 2H. (2) ("and she (Yaniara !) is twice as old as Hannah." From these two equations you get T + 3 = 2H. (3) We also have one more condition: "Tim is 2 years older than Hannah." It means that T = H + 2. (4) Substitute the expression T = H + 2 into (3). You will get (H + 2) + 3 = 2H, or 2 + 3 = 2H - H, or H = 5. So, you found that Hannah is 5 years old. Then Tim is 5 + 2 = 7 years old. Then Yaniara is T + 3 = 7 + 3 = 10 years old. Answer. Hannah is 5, Tim is 7, Yaniara is 10 years old.

Solved.

1.   This problem is SIMPLE.

2.   It is not about writing and solving a system of three equations in three unknowns!!!

3.   It is about correct and reasonable choice the major and appropriate unknowns.

4.   Finally, it is about attentive reading and understanding the condition.

5, 6, 7.   This is the LESSON TO LEARN from the solution.

Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

Yaniara is 3 years older than Tim and she is twice as old as Hannah. Tim is 2 years older than Hannah. How old are Yanaira, Tim and Hannah?
I believe
X = Tim's age
X+3 = Yaniars age
X-2 = Hannah
Trying to help my daughter with homework problem. I am sorry I am not good with these

You're very, very CORRECT.
With X being Tim's age, Yanaira's age must be X + 3, since Yanaira is 3 years older than Tim
Also, Hannah's age is definitely X - 2 since Tim is 2 years older than her, which makes her 2 years YOUNGER than Tim
Great job in setting up these polynomials!!
You missed ONE polynomial though. It's also said that Yanaira is twice Hannah's age, so Yanaira's age is also: 2(X - 2), or 2X - 4
We then can say that: X + 3 = 2X - 4
X - 2X = - 4 - 3
- X = - 7
X, or Tim's age = , or
Yanaira's age: 7 + 3, or
Hannah's age: 7 - 2, or =
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