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)   (Show Source): You can put this solution on YOUR website!

Landon's age is
Violet's age is
Hannah's age is
if the sun of the ages of Landon,Violet, and their mother hann is years, we have
.....eq.1
if Landon is years older than Violet, we have
....eq.2
and, if Hannah's age is more than twice Violet's age, we have
....eq.3

go to
.....eq.1, substitute and
.....solve for





go to
....eq.3, substitute


so, Hannah is years old



Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
(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 .



SOLVING
In your head, see
Also possibly just in your head, see .

Hannah, 51.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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
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