SOLUTION: Alloy A is composed of 3 parts gold and 1 part silver. Alloy B is composed 1 part gold and 3 part silver . When combined the alloy mixture has 15 g of gold and 9 g of silver. How m

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Question 769326: Alloy A is composed of 3 parts gold and 1 part silver. Alloy B is composed 1 part gold and 3 part silver . When combined the alloy mixture has 15 g of gold and 9 g of silver. How many grams does each alloy weight?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = total grams of alloy A
Let +b+ = total grams of alloy B
(1) +a+%2B+b+=+15+%2B+9+
(1) +a+%2B+b+=+24+
(2) +%283%2F4%29%2Aa+%2B+%281%2F4%29%2Ab+=+15+
(3) +%28+1%2F4%29%2Aa+%2B+%283%2F4%29%2Ab+=+9+
--------------------------
(2) +3a+%2B+b+=+60+
(3) +a+%2B+3b+=+36+
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Subtract (1) from (2)
(2) +3a+%2B+b+=+60+
(1) +-a+-+b+=+-24+
+2a+=+36+
+a+=+18+
and
(3) +a+%2B+3b+=+36+
(3) +18+%2B+3b+=+36+
(3) +3b+=+18+
(3) +b+=+6+
Alloy A weighs 18 g
Alloy B weighs 6 g
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check:
(1) +a+%2B+b+=+24+
(1) +18+%2B+6+=+24+
(1) +24+=+24+
OK