Jerry is presently twice as old as his brother and six years older than his sister. How many years from now will Jerry's age be $\frac{2}{3}$ of the combined ages of his brother and sister at that time?
+128473
Let Jerry's brother now be A years old
Then Jerry's age now = 2A
And his sisters age now = 2A - 6
And let x be the number of years from now when Jerry's age = (2/3) combined age of his brother and sister.....so we have that
(2A + x) = (2/3) [ (A + x) + ( 2A - 6 + x )] simplify
2A + (3/2)x = (2/3) [ 3A + 2x - 6 ] multiply through by 3/2
3A + (3/2)x = 3A + 2x - 6 subtract 3A from both sides
(3/2)x = 2x - 6 subtract 2x from both sides
-1/2x = -6 divide both sides by -1/2
x = 12 years
