SOLUTION: Eleven years from now, Peter's age will be half the square of the age he was 13 years ago. Calculate the current age of Peter.

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Eleven years from now, Peter's age will be half the square of the age he was 13 years ago. Calculate the current age of Peter.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1079108: Eleven years from now, Peter's age will be half the square of the age he was 13 years ago. Calculate the current age of Peter.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = Peter's current age
given:
+x+%2B+11+=+%281%2F2%29%2A%28+x+-+13+%29%5E2+
+2%2A%28+x+%2B+11+%29+=+x%5E2+-+26x+%2B+169+
+2x+%2B+22+=+x%5E2+-+26x+%2B+169+
+x%5E2+-28x+%2B+147+=+0+
Use quadratic equation
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-28+
+c+=+147+
----------------
+x+=+%28+-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2-4%2A1%2A147+%29%29%2F%282%2A1%29+
+x+=+%28+28+%2B-+sqrt%28+784+-+588+%29%29%2F2+
+x+=+%28+28+%2B-+sqrt%28+196+%29%29%2F2+
+x+=+%28+28+%2B+14+%29+%2F+2+
+x+=+42%2F2+
+x+=+21+
Peter is 21 now
------------------
check:
+x+%2B+11+=+%281%2F2%29%2A%28+x+-+13+%29%5E2+
+21+%2B+11+=+%281%2F2%29%2A%28+21+-+13+%29%5E2+
+32+=+%281%2F2%29%2A8%5E2+
+32+=+%281%2F2%29%2A64+
+32+=+32+
OK
I'll try the negative root of +196+ also
+x+=+%28+28+-+14+%29+%2F+2+
+x+=+14%2F2+
+x+=+7+
-----------------
+x+%2B+11+=+%281%2F2%29%2A%28+x+-+13+%29%5E2+
+7+%2B+11+=+%281%2F2%29%2A%28+7+-+13+%29%5E2+
+18+=+%281%2F2%29%2A%28+-6+%29%5E2+
+18+=+%281%2F2%29%2A36+
+18+=+18+
I don't think this is a valid solution since his
age 13 years ago ends up being 6 years
before he was born. I'll stick with
the 1st answer.