Question 1163312
s = sarah's age now.
l = linda's age now.
sarah is currently 4 times as old as linda.
that gets you:
s = 4 * l
in 6 years, sarah will be 3 times as old as linda.
that gets you:
s + 6 = 3 * (l + 6)
simplify this equation and subtact 6 from both sides to get:
s = 3 * l + 12
since s = 4 * l from the first equation, replace s with 4 * l to get:
4 * l = 3 * l + 12
solve for l to get:
l = 12
s = 4 * l = 48
in 6 years s is 54 and l is 18.
at that time, s = 3 * l because 3 * 18 = 54.


be careful how your word your problem.
3 times as old is not the same as 3 times older.
if the current age is 10, then 3 times as old makes the new age equal to 30 which is 20 more than 10 which is 2 times older than 10.
if the current age is 10, then 3 times older makes the new age equal to 40 which is 30 more than 10 which is 3 times older than 10, but 4 times as old as 10.


to put it another way:
y = 3x means y is 3 times as large as x.
y = 3x + x means y is 3 times larger than x which means that y = 4 times as much as x.


your problem works with 3 times as much.
it does not work with 3 times larger because 3 times larger means 4 times as large.
solve for 3 times larger, you get:
y = 4x
y + 6 = 3 * (x + 6) + (x + 6) which becomes y + 6 = 4 * (x + 6) which becomes y + 6 = 4 * x + 24 which becomes y = 4 * x + 18
y = 4 * x and y = 4 * x + 18 yield two straight line equations that have the same slope, therefore parallel to each other, therefore will never intersect, so there's no way to solve for x.
on the other hand, y + 6 = 3 * (x + 6) gets you y + 6 = 3 * x + 18 which results in y = 3 * x + 12 and, since y = 4 * l, you get 4 * l = 3 * l + 12 which results in x = 12.