SOLUTION: Mrs. G thinks a slightly altered version of the same medicine might very well clear up her gooey scalp. Now she is mixing a liquid containing 12% reactor fuel with a liquid contai

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Question 1158390: Mrs. G thinks a slightly altered version of the same medicine might very well clear up her gooey scalp. Now she is mixing a liquid containing 12% reactor fuel with a liquid containing 32% reactor fuel to create a 4 ounce liquid containing 20% reactor fuel. How many ounces of the 12% liquid must she use? Round to the nearest one decimal place(tenths).
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 12% mixture needed
Let +b+ = ounces of 32% mixture needed
-----------------------------------------------------
(1) +a+%2B+b+=+4+
(2) +%28+.12a+%2B+.32b+%29+%2F+4+=+.2+
--------------------------------------
(2) +.12a+%2B+.32b+=+.8+
(2) +12a+%2B+32b+=+80+
(2) +3a+%2B+8b+=+20+
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3a+%2B+8b+=+20+
(1) +-3a+-+3b+=+-12+
----------------------------
+5b+=+8+
+b+=+1.6+
and
(1) +a+%2B+b+=+4+
(1) +a+%2B+1.6+=+4+
(1) +a+=+2.4+
She must use 2.4 ounces of the 12% liquid
----------------------------
check:
(2) +%28+.12a+%2B+.32b+%29+%2F+4+=+.2+
(2) +%28+.12%2A2.4+%2B+.32%2A1.6+%29+%2F+4+=+.2+
(2) +%28+.288+%2B+.512+%29+%2F+4+=+.2+
(2) +.8+=+.2%2A4+
(2) +.8+=+.8+
OK

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Mrs. G thinks a slightly altered version of the same medicine might very well clear up her gooey scalp. Now she is mixing a liquid containing 12% reactor fuel with a liquid containing 32% reactor fuel to create a 4 ounce liquid containing 20% reactor fuel. How many ounces of the 12% liquid must she use? Round to the nearest one decimal place(tenths).
Let amount of 12% liquid to mix, be T

Then amount of the 32% liquid is, 4 - T

We then get: .12T + .32(4 - T) = .2(4)

.12T + 1.28 - .32T = .8

.12T - .32T = .8 - 1.28

- .2T = - .48

Amount of 12% liquid to mix, or