SOLUTION: The sun of the ages of Landon,Violet, and their mother hann is 104 years. Landon is 3 years older than Violet, and Hannah's age is 1 more than twice Violet's age. How old is Hannah

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Question 1203878: The sun of the ages of Landon,Violet, and their mother hann is 104 years. Landon is 3 years older than Violet, and Hannah's age is 1 more than twice Violet's age. How old is Hannah?
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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Landon's age is L
Violet's age is V
Hannah's age is H
if the sun of the ages of Landon,Violet, and their mother hann is 104 years, we have
L%2BV%2BH=104.....eq.1
if Landon is 3 years older than Violet, we have
L=V%2B3....eq.2
and, if Hannah's age is 1 more than twice Violet's age, we have
H=2V%2B1....eq.3

go to
L%2BV%2BH=104.....eq.1, substitute L and H
V%2B3%2BV%2B2V%2B1=104.....solve for V
4V%2B4=104
4V=104-4
4V=100
V=100%2F4
V=25
go to
H=2V%2B1....eq.3, substitute V
H=2%2A25%2B1
H=+51
so, Hannah is +51 years old



Answer by josgarithmetic(39620) About Me  (Show Source):
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(Assuming not "Hann", but "Hannah")

Three unknown variables. Try to use fewer unknown variables. 
Landon           v+3
Violet            v
Hannah            2v+1
SUM              104

May be easiest way to analyze and arrange. Question asks for 2v%2B1.



SOLVING
In your head, see 4v%2B4=104
Also possibly just in your head, see v=25.

Hannah, 51.

Answer by greenestamps(13200) About Me  (Show Source):
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You are making a lot of extra work for yourself setting up the problem using three variables, as the other tutor did.

The statement of the problem makes it easy to set it up using a single variable, making the path to the solution much easier.

Let x = Violet's age
Then x+3 = Landon's age
And 2x+1 = Hannah's age

The sum of their ages is 104:

x+x+3+2x+1 = 104
4x+4 = 104
4x = 100
x = 25

ANSWER: Hannah's age is 2x+1 = 51