Question 970179: Johnny is now two fifth of his older brother's age and two years from now he will be half of his older brother's age. Two years ago, Johnny was only one fourth the ago of his older brother. How old is Johnny now ?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Johnny is now two fifth of his older brother's age and two years from now he will be half of his older brother's age.
Two years ago, Johnny was only one fourth the ago of his older brother.
How old is Johnny now ?
:
let j = John's age
let b = brother's age
:
Write an equation for each statement, we can use decimals for the fractions here
:
"Johnny is now two fifth of his older brother's age"
j = .4b
and two years from now he will be half of his older brother's age.
j + 2 = .5(b+2)
j + 2 = .5b + 1
j = .5b + 1 - 2
j = .5b - 1
"Two years ago, Johnny was only one fourth the ago of his older brother."
j - 2 = .25(b-2)
j - 2 = .25b - .5
j = .25b - .5 + 2
j = .25b + 1.5
replace j with .4b, fro the 1st statement
.4b = .25b + 1.5
.4b - .25b = 1.5
.15b = 1.5
b = 1.5/.15
b = 10 yrs old is brother's age
then
j = .4(10)
j = 4 yrs old is John's age
:
:
Check our solutions in the 2nd statement
"Johnny, two years from now he will be half of his older brother's age."
4 + 2 = .5(10 + 2)
How old is Johnny now ? 4 yrs
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