SOLUTION: Hi. I have a word problem that I just can't wrap my head around. Could you please help me? "Professor Baird wants to mix a solution containing 10% acid with one containing 15%

Algebra ->  Average -> SOLUTION: Hi. I have a word problem that I just can't wrap my head around. Could you please help me? "Professor Baird wants to mix a solution containing 10% acid with one containing 15%       Log On


   



Question 588182: Hi. I have a word problem that I just can't wrap my head around. Could you please help me?
"Professor Baird wants to mix a solution containing 10% acid with one containing 15% acid to obtain a 20-ounce solution containing 12% acid. How many ounces of the 10% solution should the professor use?"
Thanks for the help.
Joey

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 10% solution needed
Let +b+ = ounces of 15% solution needed
+.1a+ = ounces of acid in 10% solution
+.15b+ = ounces of acid in 15% solution
---------------------------------
(1) +a+%2B+b+=++20+
(2) +%28+.1a+%2B+.15b+%29+%2F+20+=+.12+
-------------------------
(2) +.1a+%2B+.15b+=+.12%2A20+
(2) +.1a+%2B+.15b+=+2.4+
(2) +10a+%2B+15b+=+240+
--------------------
Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10a+%2B+15b+=+240+
(1) +-10a+-+10b+=+-200+
+5b+=+40+
+b+=+8+
and, since
+a+%2B+b+=+20+
+a+%2B+8+=+20+
+a+=+12+
12 ounces of 10% solution is needed
8 ounces of 15% solution is needed
check:
(2) +%28+.1a+%2B+.15b+%29+%2F+20+=+.12+
(2) +%28+.1%2A12+%2B+.15%2A8+%29+%2F+20+=+.12+
(2) +%28+1.2+%2B+1.2+%29+%2F+20+=+.12+
(2) +2.4+%2F+20+=+.12+
(2) +2.4+=+2.4+
OK