SOLUTION: Joe's brother is 6 years older than Joe. Two-thirds of his brother's age is 3 years more than three-fourths of his age. How old is Joe?

Question 849671: Joe's brother is 6 years older than Joe. Two-thirds of his brother's age is 3 years more than three-fourths of his age. How old is Joe?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let j = Joe's age
let b = brother's age
:
Write an equation for each statement:
"Joe's brother is 6 years older than Joe."
b = j + 6
" Two-thirds of his brother's age is 3 years more than three-fourths of his age."
b = j + 3
Multiply by 12 to get rid of the denominators, then you have:
8b = 9j + 36
Replace b with (j+6) from the 1st statement
8(j+6) = 9j + 36
8j + 48 = 9j + 36
48 - 36 = 9j - 8j
12 = j
How old is Joe? 12 yrs old
:
:
Check this, we know brother is 18 then
Two-thirds of his brother's age is 3 years more than three-fourths of his age."
(18) = (12) + 3
12 = 9 + 3; confirms our solution

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