SOLUTION: Please help me solve this word problem, using substitution or elimination: How much of a perfume that sells for $35 dollar per ounce should be mixed with a perfume that sells fo

Algebra ->  Equations -> SOLUTION: Please help me solve this word problem, using substitution or elimination: How much of a perfume that sells for $35 dollar per ounce should be mixed with a perfume that sells fo      Log On


   



Question 1025105: Please help me solve this word problem, using substitution or elimination:
How much of a perfume that sells for $35 dollar per ounce should be mixed with a perfume that sells for $15 dollar per ounce to make a 3-ounce bottle of perfume that can be sold for $63?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of $35/oz perfume needed
Let +b+ = ounces of $15/oz perfume needed
---------------------------------------
+63%2F3+=+21+
Perfume selling for $21/oz is desired
(1) +a+%2B+b+=+3+
(2) +%28+35a+%2B+15b+%29+%2F+3+=+21+
---------------------------
(2) +35a+%2B+15b+=+63+
Multiply both sides of (1) by +15+ and
subtract (1) from (2)
(2) +35a+%2B+15b+=+63+
(1) +-15a+-+15b+=+-45+
-----------------------
+20a+=+18+
+a+=+.9+
and
(1) +.9+%2B+b+=+3+
(1) +b+=+2.1+
-----------------
0.9 ounces of $35/oz perfume is needed
2.1 ounces of $15/oz perfume is needed
----------------------------------
check:
(2) +%28+35a+%2B+15b+%29+%2F+3+=+21+
(2) +%28+35%2A.9+%2B+15%2A2.1+%29+%2F+3+=+21+
(2) +%28+31.5+%2B+31.5+%29+%2F+3+=+21+
(2) +63%2F3+=+21+
(2) +63+=+63+
OK