SOLUTION: A pharmacist wants to make 18 ml of a 6% hydrogen peroxide solution. How many mls of 5% hydrogen peroxide must he mix with 7% hydrogen peroxide to make the desired solution?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A pharmacist wants to make 18 ml of a 6% hydrogen peroxide solution. How many mls of 5% hydrogen peroxide must he mix with 7% hydrogen peroxide to make the desired solution?      Log On


   



Question 596472: A pharmacist wants to make 18 ml of a 6% hydrogen peroxide solution. How many mls of 5% hydrogen peroxide must he mix with 7% hydrogen peroxide to make the desired solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 5% solution needed
Let +b+ = ml of 7% solution needed
+.05a+ = ml of hydrogen peroxide in 5% solution
+.07b+ = ml of hydrogen peroxide in 7% solution
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given:
(1) +a+%2B+b+=+18+
(2) +%28+.05a+%2B+.07b+%29+%2F+18+=+.06+
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(2) ++.05a+%2B+.07b++=+.06%2A18+
(2) ++.05a+%2B+.07b++=+1.08+
(2) +5a+%2B+7b+=+108+
Multiply both sides of (1) by 5 and
subtract (1) from (2)
(2) +5a+%2B+7b+=+108+
(1) +-5a+-+5b+=+-90+
+2b+=+18+
+b+=+9+
and, since
(1) +a+%2B+b+=+18+
(1) +a+%2B+9+=+18+
(1) +a+=+9+
9 ml of 5% solution is needed
9 ml of 7% solution is needed
check:
(2) +%28+.05a+%2B+.07b+%29+%2F+18+=+.06+
(2) +%28+.05%2A9+%2B+.07%2A9+%29+%2F+18+=+.06+
(2) +%28+.45+%2B+.63+%29+%2F+18+=+.06+
(2) +1.08+%2F+18+=+.06+
(2) +1.08+=+.06%2A18+
(2) +1.08+=+1.08+
OK