SOLUTION: A mixture of 15% disinfectant solution is to be made from 13% and 18% disinfectant solution. How much of each solution should be used if 20gallons of the 15% solution are needed?

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Question 1051796: A mixture of 15% disinfectant solution is to be made from 13% and 18% disinfectant solution. How much of each solution should be used if
20gallons of the 15% solution are needed?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of the 13% mixture needed
Let +b+ = gallons of the 18% mixture needed
--------------------------------------------
(1) +%28+.13a+%2B+.18b+%29+%2F+20+=+.15+
(2) +a+%2B+b+=+20+
----------------------------------
(1) +.13a+%2B+.18b+=++.15%2A20+
(1) +.13a+%2B+.18b+=+3+
(1) +13a+%2B+18b+=+300+
------------------------------
Multiply both sides of (2) by +13+
and subtract (2) from (1)
-----------------------------------
(1) +13a+%2B+18b+=+300+
(2) +-13a+-+13b+=+-260+
----------------------------
+5b+=+40+
+b+=+8+
and
(2) +a+%2B+8+=+20+
(2) +a+=+12+
12 gallons of the 13% mixture are needed
8 gallons of the 18% mixture are needed
---------------------------------------
check:
(1) +%28+.13a+%2B+.18b+%29+%2F+20+=+.15+
(1) +%28+.13%2A12+%2B+.18%2A8+%29+%2F+20+=+.15+
(1) +%28+1.56+%2B+1.44+%29+%2F+20+=+.15+
(1) +3%2F20+=+.15+
(1) +3+=+.15%2A20+
(1) +3+=+3+
OK