SOLUTION: 2)Ryan was born 6 and one-fourth years after Alexander.The sum of their ages are 66 and eleven-twelfth years.How old are Alexander and Ryan?

Question 164507: 2)Ryan was born 6 and one-fourth years after Alexander.The sum of their ages are 66 and eleven-twelfth years.How old are Alexander and Ryan?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
2)Ryan was born 6 and one-fourth years after Alexander.The sum of their ages are 66 and eleven-twelfth years.How old are Alexander and Ryan?
:
Man, they love these fractions, don't they
:
Let r = Ryan's age now
Let a = Alexander's age now
:
Write an equation for each statement:
:
"Ryan was born 6 and one-fourth years after Alexander."
r = a - 6
Convert to an improper fraction
r = a -
Get rid of the fraction, mult by 4
4r = 4a - 25
or
4a - 4r = 25
:
"The sum of their ages are 66 and eleven-twelfth years."
a + r = 66
convert to an improper fraction
a + r =
Get rid of the fraction, mult by 12
12a + 12r = 803
:
Multiply eq (4a-4r=25) by 3 and add to the above equation
12a + 12r = 803
12a - 12r = 75
------------------adding eliminates r, find a
24a = 878
a = 36
a = 36 is Alexander's age
:
Find r using equation: a + r = 66
r = 66 - 36
r = 30
r = 30; is Ryan's age
;
:
Confirm our solutions using the original equation: r = a - 6
30 = 36 - 6
30 = 30

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