SOLUTION: A grocer is mixing 80 cent per kg coffee with $1.20 per kg coffee to make a mixture worth $1.08 per kg. How much of each kind of coffee should be used to make 70 kg of the mixtur

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Question 939413: A grocer is mixing 80 cent per kg coffee with $1.20 per kg coffee to
make a mixture worth $1.08 per kg. How much of each kind of coffee should be used to make
70 kg of the mixture?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kg of $.80/kg coffee needed
Let +b+ = kg of $1.20/kg coffee needed
--------------------------------------
(1) +a+%2B+b+=+70+
(2) +%28+.8a+%2B+1.2b+%29+%2F+70+=+1.08+
--------------------------------
(2) +.8a+%2B+1.2b+=+1.08%2A70+
(2) +.8a+%2B+1.2b+=+75.6+
(2) +8a+%2B+12b+=+756+
(2) +2a+%2B+3b+=+189+
---------------------
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2a+%2B+3b+=+189+
(1) +-2a+-+2b+=+-140+
------------------------
+b+=+49+
and
(1) +a+%2B+b+=+70+
(1) +a+=+21+
----------------
21 kg of $.80/kg coffee are needed
49 kg of $1.20/kg coffee are needed
check:
(2) +%28+.8%2A21+%2B+1.2%2A49+%29+%2F+70+=+1.08+
(2) +%28+16.8+%2B+58.8+%29+%2F+70+=+1.08+
(2) +75.6+=+75.6+
OK