SOLUTION: An engine has a 6.6 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 57.6 % solution (a mix of 57.6 % pure antifreeze and 42.4 % wate

Algebra ->  Matrices-and-determiminant -> SOLUTION: An engine has a 6.6 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 57.6 % solution (a mix of 57.6 % pure antifreeze and 42.4 % wate      Log On


   

Question 716949:
An engine has a 6.6 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 57.6 % solution (a mix of 57.6 % pure antifreeze and 42.4 % water). How much pure antifreeze (in litres) must be combined with a 29.4 % solution to achieve 6.6 litres of the ideal solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of pure antifreeze to be used
Let +b+ = liters of 29.4% solution to be used
+.294b+ = liters of pure antifreeze in 29.4% solution
---------------
given:
(1) +a+%2B+b+=+6.6+
(2) +%28+a+%2B+.294b+%29+%2F+6.6+=+.576+
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(2) +a+%2B+.294b+=+.576%2A6.6+
(2) +a+%2B+.294b+=+3.8016+
(2) +1000a+%2B+294b+=+3802+
Multiply both sides of (1) by +294+ and
subtract (1) from (2)
(2) +1000a+%2B+294b+=+3802+
(1) +-294a+-+294b+=+-1940+
+706a+=+1862+
+a+=+2.6374+
and, since
(1) +2.6374+%2B+b+=+6.6+
(1) +b+=+3.9626+
2.6374 liters of pure antifreeze must be used
check answer:
(2) +%28+2.6374+%2B+.294%2A3.9626+%29+%2F+6.6+=+.576+
(2) +%28+2.6374+%2B+1.1650+%29+%2F+6.6+=+.576+
(2) +3.8024+%2F+6.6+=+.576+
(2) +3.8024+=+3.8016+
OK- I think error is due to rounding off