SOLUTION: How Much Tin and how much lead must be added to 700 pounds of an alloy containing 50% tin and 25% lead to make an alloy which is 60% tin and 20% lead?

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Question 625725: How Much Tin and how much lead must be added to 700 pounds of an alloy containing 50% tin and 25% lead to make an alloy which is 60% tin and 20% lead?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of tin to be added
Let +b+ = pounds of lead to be added
+.5%2A700+=+350+ pounds of tin in original alloy
+.25%2A700+=+175+ pounds of lead in original alloy
----------------
given:
(1) +%28+a+%2B+350+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.6+
(2) +%28+b+%2B+175+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.2+
----------------------------
(1) +a+%2B+350+=+.6%2A%28+a+%2B+b+%2B+700+%29+
(1) +a+%2B+350+=+.6a+%2B+.6b+%2B+420+
(1) +.4a+-+.6b+=+420+-+350+
(1) +.4a+-+.6b+=+70+
(1) +4a+-+6b+=+700+
and
(2) +%28+b+%2B+175+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.2+
(2) +b+%2B+175+=+.2%2A%28+a+%2B+b+%2B+700+%29+
(2) +b+%2B+175+=+.2a+%2B+.2b+%2B+140+
(2) +.8b+-+.2a++=+140+-+175+
(2) +.8b+-+.2a+=+-35+
(2) +2a+-+8b+=+350+
Multiply both sides of (2) by 2
and subtract (2) from (1)
(1) +4a+-+6b+=+700+
(2) +-4a+%2B+16b+=+-700+
+10b+=+0+
+b+=+0+
and, since
(2) +2a+-+8b+=+350+
(2) +2a+-+8%2A0+=+350+
(2) +2a+=+350+
(2) +a+=+175+
175 pounds of tin should be added and
no lead should be added
check answer:
(1) +%28+a+%2B+350+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.6+
(1) +%28+175+%2B+350+%29+%2F+%28+175+%2B+0+%2B+700+%29+=+.6+
(1) +525+%2F+875+=+.6+
(1) +21%2F35+=+.6+
(1) +21+=+21+
OK
(2) +%28+b+%2B+175+%29+%2F+%28+a+%2B+b+%2B+700+%29+=+.2+
(2) +%28+0+%2B+175+%29+%2F+%28+175+%2B+0+%2B+700+%29+=+.2+
(2) +175+%2F+875+=+.2+
(2( +175+=+175+
OK