SOLUTION: A baker is making fudge and his recipe calls for thirty 75% cocoa chocolate squares. He looks in his cupboard to discover he only has 60% cocoa and 85% cocoa. How many of each sho

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Question 843740: A baker is making fudge and his recipe calls for thirty 75% cocoa chocolate squares. He looks in his cupboard to discover he only has 60% cocoa and 85% cocoa. How many of each should he use to make his fudge?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have enough 60% fudge to make +a+ squares
You have enough 85% fudge to make +b+ squares
(1) +a+%2B+b+=+30+
(2) +%28+.6a+%2B+.85b+%29+%2F+30+=+.75+
-----------------------------
(2) +.6a+%2B+.85b+=+.75%2A30+
(2) +.6a+%2B+.85b+=+22.5+
(2) +60a+%2B+85b+=+2250+
Multiply both sides of (1) by +60+
and subtract (1) from (2)
(2) +60a+%2B+85b+=+2250+
(1) +-60a+-+60b+=+-1800+
+25b+=+450+
+b+=+18+
and
(1) +a+=+30+-+b+
(1) +a+=+30+-+18+
(1) +a+=+12+
He needs enough of the 60% cocoa for 12 squares
He needs enough of the 85% cocoa for 18 squares
check:
(2) +%28+.6a+%2B+.85b+%29+%2F+30+=+.75+
(2) +%28+.6%2A12+%2B+.85%2A18+%29+%2F+30+=+.75+
(2) +%28+7.2+%2B+15.3+%29+%2F+30+=+.75+
(2) +7.2+%2B+15.3+=+.75%2A30+
(2) +22.5+=+22.5+
OK