SOLUTION: Mary is mixing up some punch for her party tomorrow. She messed up at first and ended up with two different punches, one that was too strong and one that was too weak. The first wa

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Question 751561: Mary is mixing up some punch for her party tomorrow. She messed up at first and ended up with two different punches, one that was too strong and one that was too weak. The first was too weak, 20 liters of an 18% punch mix and the second was too strong, 50 liters of a 30% mix. She wanted all the punch to have 25% punch mix. How can she mix what she has with water to create the proper punch?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Interesting you ask, how much water.

If that is how the adjustment is to be done, then ignore the 18% punch and just use the 30% punch.
50%2A30%2F%2850%2Bw%29=25 where w is how much liters of water to add. Solve for w.

25%2850%2Bw%29=1500
25%2A50%2B25w=1500
25w=1500-25%2A50
25w=250
highlight%28w=10%29 liters water

Certainly there are other ways, such as to use some or (maybe) all(?) of the 18% punch along with the 30%.

A good alternative is say, let e be how much of the 18% punch to add to the 50 liter of 30% punch. Add no extra water.
... in fact, you would need to add ALL of the 20 liters of the 18% plus some water.
...
highlight%28%2850%2A30%2B20%2A18%29%2F%2850%2B20%2Bw%29=25%29
Solve for w, the liters of water to add to ALL of the available punch solutions.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+.18%2A20+=+3.6+ = liters of punch in 18% punch mix
+.3%2A50+=+15+ = liters of punch in 30% punch mix
Let +w+ = liters of water to be added to get 25% punch mix
-----------------------------------------------------
+%28+3.6+%2B+15+%29+%2F+%28+20+%2B+50+%2B+w+%29+=+.25+
+18.6+%2F+%28+70+%2B+w+%29+=+.25+
+18.6+=+.25%2A%28+70+%2B+w+%29+
+18.6+=+17.5+%2B+.25w+
+.25w+=+1.1+
+w+=+4.4+
4.4 liters of water should be added
check:
+18.6+%2F+%28+70+%2B+w+%29+=+.25+
+18.6+%2F+%28+70+%2B+4.4+%29+=+.25+
+18.6+=+.25%2A74.4+
+18.6+=+18.6+
OK