SOLUTION: Suppose you have a supply of a 25% solution of alcohol and a 75% solution Of alcohol. How Many quarts of Each Should be mixed to produce 40 quarts that is 70% produce? I need help

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Suppose you have a supply of a 25% solution of alcohol and a 75% solution Of alcohol. How Many quarts of Each Should be mixed to produce 40 quarts that is 70% produce? I need help       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 779078: Suppose you have a supply of a 25% solution of alcohol and a 75% solution Of alcohol. How Many quarts of Each Should be mixed to produce 40 quarts that is 70% produce? I need help setting this problem up.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = quarts of 25% alcohol solution needed
Let +b+ = quarts of 75% alcohol solution needed
---------------
(1) +a+%2B+b+=+40+
(2) +%28+.25a+%2B+.75b+%29+%2F+40+=+.7+
----------------------------
(2) +.25a+%2B+.75b+=+.7%2A40+
(2) +.25a+%2B+.75b+=+28+
(2) +25a+%2B+75b+=+2800+
Multiply both sides of (1) by +25+ and subtract
(1) from (2)
(2) +25a+%2B+75b+=+2800+
(1) +-25a+-+25b+=+-1000+
+50b+=+1800+
+b+=+36+
and, since
(1) +a+%2B+b+=+40+
(1) +a+=+4+
---------------
4 quarts of 25% alcohol solution are needed
36 quarts of 75% alcohol solution are needed
---------------
check:
(2) +%28+.25%2A4+%2B+.75%2A36+%29+%2F+40+=+.7+
(2) +%28+1+%2B+27+%29+%2F+40+=+.7+
(2) +28+=+.7%2A40+
(2) +28+=+28+
OK