SOLUTION: A printer has ink that is 13% cobalt blue color and ink that is 17% cobalt blue color. How many ounces of each ink are needed to make 2 gallons (256 ounces) of ink that is 15% coba

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Question 760543: A printer has ink that is 13% cobalt blue color and ink that is 17% cobalt blue color. How many ounces of each ink are needed to make 2 gallons (256 ounces) of ink that is 15% cobalt blue color
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 13% ink needed
Let +b+ = ounces of 17% ink needed
+.13a+ = ounces of cobalt blue color in 13% ink
+.17b+ = ounces of cobalt blue color in 17% ink
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(1) +a+%2B+b+=+256+
(2) +%28+.13a+%2B+.17b+%29+%2F+256+=+.15+
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(2) +.13a+%2B+.17b+=+.15%2A256+
(2) +.13a+%2B+.17b+=+38.4+
(2) +13a+%2B+17b+=+3840+
Multiply both sides of (1) by +13+
and subtract (1) from (2)
(2) +13a+%2B+17b+=+3840+
(1) +-13a+-+13b+=+-3328+
+4b+=+512+
+b+=+128+
and, since
(1) +a+%2B+b+=+256+
(1) +a+%2B+128+=+256+
(1) +a+=+128+
128 ounces of 13% ink are needed
128 ounces of 17% ink are needed
check:
(2) +%28+.13%2A128+%2B+.17%2A128+%29+%2F+256+=+.15+
(2) +%28+16.64+%2B+21.76+%29+%2F+256+=+.15+
(2) +38.4+=+.15%2A256+
(2) +38.4+=+38.4+
OK