Answer Below:
Sorry for the late notice, but here you go:
Let +a+ = liters of 15% solution needed
Let +b+ = liters of 35% solution needed
Let +c+ = liters of 80% solution needed
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(1) +a+%2B+b+%2B+c+=+100+
(2) +c+=+2b+
(3) +%28+.15a+%2B+.35b+%2B+.8c+%29+%2F+100+=+.3+
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(3) +.15a+%2B+.35b+%2B+.8c+=+30+
(3) +15a+%2B+35b+%2B+80c++3000+
(3) +3a+%2B+7b+%2B+16c+=+600+
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Multiply both sides of (1) by +3+ and
subtract (1) from (3)
(3) +3a+%2B+7b+%2B+16c+=+600+
(1) +-3a+-+3b+-+3c+=+-300+
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+4b+%2B+13c+=+300+
Substitute (2) into this result
+4b+%2B+13%2A%282b%29+=+300+
+4b+%2B+26b+=+300+
+30b+=+300+
+b+=+10+
and
(2) +c+=+2b+
(2) +c+=+2%2A10+
(2) +c+=+20+
and
(1) +a+%2B+10+%2B+20+=+100+
(1) +a+=+100+-+30+
(1) +a+=+70+
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70 liters of 15% solution is needed
10 liters of 35% solution is needed
20 liters of 80% solution is needed
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check:
(3) +%28+.15a+%2B+.35b+%2B+.8c+%29+%2F+100+=+.3+
(3) +%28+.15%2A70+%2B+.35%2A10+%2B+.8%2A20+%29+%2F+100+=+.3+
(3) +%28+10.5+%2B+3.5+%2B+16+%29+%2F+100+=+.3+
(3) +10.5+%2B+3.5+%2B+16+=+30+
(3) +30+=+30+
Hope this helped!