SOLUTION: A printer has ink that is 3% cobalt blue color and ink that is 7% cobalt blue color. How many ounces of each ink are needed to make 2 gallons (256 ounces) of ink that is 5% cobalt

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Question 1067513: A printer has ink that is 3% cobalt blue color and ink that is 7% cobalt blue color. How many ounces of each ink are needed to make 2 gallons (256 ounces) of ink that is 5% cobalt blue color?
3% cobalt blue color_________oz    


7% cobalt blue color__________oz    


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 3% cobalt blue color needed
Let +b+ = ounces of 7% cobalt blue color needed
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(1) +a+%2B+b+=+256+
(2) +%28+.03a+%2B+.07b+%29+%2F+256+=+.05+
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(2) +.03a+%2B+.07b+=+.05%2A256+
(2) +.03a+%2B+.07b+=+12.8+
(2) +3a+%2B+7b+=+1280+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3a+%2B+7b+=+1280+
(1) +-3a+-+3b+=+-768+
--------------------------
+4b+=+512+
+b+=+128+
and
(1) +a+%2B+b+=+256+
(1) +a+%2B+128+=+256+
(1) +a+=+128+
--------------------
128 ounces of 3% cobalt blue color are needed
128 ounces of 7% cobalt blue color are needed
--------------------
check:
(2) +%28+.03a+%2B+.07b+%29+%2F+256+=+.05+
(2) +%28+.03%2A128+%2B+.07%2A128+%29+%2F+256+=+.05+
(2) +%28+3.84+%2B+8.96+%29+%2F+256+=+.05+
(2) +12.8+=+.05%2A256+
(2) +12.8+=+12.8+
OK