SOLUTION: mom made 2 batches of iced tea. 1st batch was 6% sugar and was too sweet, the 2nd batch was 3% sugar and was not sweet enough. how many cups should she take from each batch to make

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Question 621229: mom made 2 batches of iced tea. 1st batch was 6% sugar and was too sweet, the 2nd batch was 3% sugar and was not sweet enough. how many cups should she take from each batch to make 9 cups of iced tea containing 4% sugar?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of cups of 6% tea needed
Let +b+ = number of cups of 3% tea needed
+.06a+ = cups of sugar in 6% tea
+.03b+ = cups of sugar in 3% tea
-----------
(1) +a+%2B+b+=+9+
(2) +%28+.06a+%2B+.03b+%29+%2F+9+=+.04+
-------------------------
(2) +.06a+%2B+.03b+=+.36+
(2) +6a+%2B+3b+=+36+
(2) +2a+%2B+b+=+12+
Subtract (1) from (2)
(2) +2a+%2B+b+=+12+
(1) +-a+-+b+=+-9+
+a+=+3+
and, since
(1) +a+%2B+b+=+9+
(1) +3+%2B+b+=+9+
(1) +b+=+6+
3 cups of 6% tea are needed
6 cups of 3% tea are needed
check:
(2) +%28+.06a+%2B+.03b+%29+%2F+9+=+.04+
(2) +%28+.06%2A3+%2B+.03%2A6+%29+%2F+9+=+.04+
(2) +%28+.18+%2B+.18+%29+%2F+9+=+.04+
(2) +.36%2F9+=+.04+
(2) +.36+=+.04%2A9+
(2) +.36+=+.36+
OK