SOLUTION: Joey has a 25% antifreeze solution. He also has pure antifreeze. How much of the 25% solution and the pure antifreeze is needed to fill his 12- quart cooling system with a 50% anti

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Joey has a 25% antifreeze solution. He also has pure antifreeze. How much of the 25% solution and the pure antifreeze is needed to fill his 12- quart cooling system with a 50% anti      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 732067: Joey has a 25% antifreeze solution. He also has pure antifreeze. How much of the 25% solution and the pure antifreeze is needed to fill his 12- quart cooling system with a 50% antifreeze solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = quarts of 25% solution needed
Let +b+ = quarts of pure antifreeze needed
given:
(1) +a+%2B+b+=+12+
(2) +%28+.25a+%2B+b+%29+%2F+12+=+.5+
-------------------------
(2) +.25a+%2B+b+=+.5%2A12+
(2) +.25a+%2B+b+=+6+
(2) +25a+%2B+100b+=+600+
(2) +a+%2B+4b+=+24+
Subtract (1) from (2)
(2) +a+%2B+4b+=+24+
(1) +-a+-+b+=+-12+
+3b+=+12+
+b+=+4+
and, since
(1) +a+%2B+b+=+12+
(1) +a+=+8+
8 quarts of 25% solution are needed
4 quarts of pure antifreeze are needed
check:
(2) +%28+.25%2A8+%2B+4+%29+%2F+12+=+.5+
(2) +%28+2+%2B+4+%29+%2F+12+=+.5+
(2) +6%2F12+=+.5+
(2) +6+=+6+
OK