SOLUTION: kate's father is 50 years old. kate is 24 years old now. how many years ago was kate's father three times as old as her.

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Question 881803: kate's father is 50 years old. kate is 24 years old now. how many years ago was kate's father three times as old as her.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k+ = Kate's age now
+50+ = her father's age now
Kate's father is 50 years old. Kate is 24 years old now.
The difference in their ages will never change
+50+-+24+=+26+
So, I can say
+f+-+k+=+26+
+k+=+f+-+26+
Let +n+ = the number of years ago that
Kate's father was 3 times as old as her
---------------------
+f50-+n+=+3%2A%28+k+-+n+%29+
By substitution:
+50+-+n+=+3%2A%28+50+-+26+-+n+%29+
+50-+n+=+3%2A50+-+78+-+3n+
+50+-+n+=+150+-+78+-+3n+
+3n+-+n+=+150+-+78+-+50+
+2n+=+22+
+n+=+11+
11 years ago Kate's father was 3 times her age
-----------------
check:
11 years ago, father was +50+-+11+=+39+
and, 11 years ago,
+39+=+3%2Ak+
+k+=+13+
The difference in their ages was:
+39+-+13+=+26+
OK