SOLUTION: Lily went shopping with Alan. Lily spent $11.20 for 3.60 kg flour and 1 kg sugar. Alan spent $20 for 5 kg flour and 2.50 kg sugar. What is the price of a kilogram of flour and a ki

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Lily went shopping with Alan. Lily spent $11.20 for 3.60 kg flour and 1 kg sugar. Alan spent $20 for 5 kg flour and 2.50 kg sugar. What is the price of a kilogram of flour and a ki      Log On


   

Question 1105106: Lily went shopping with Alan. Lily spent $11.20 for 3.60 kg flour and 1 kg sugar. Alan spent $20 for 5 kg flour and 2.50 kg sugar. What is the price of a kilogram of flour and a kilogram of sugar respectively

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = price in dollars/kg for flour
Let +b+ = price in dollars/kg for sugar
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(1) +3.6a+%2B+1%2Ab+=+11.2+
(2) +5a+%2B+2.5b+=+20+
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(1) +36a+%2B+10b+=+112+
and
(2) +50a+%2B+25b+=+200+
--------------------------
(1) +18a+%2B+5b+=+56+
(2) +2a+%2B+b+=+8+
Multiply both sides of (2) by +5+ and
subtract (2) from (1)
(1) +18a+%2B+5b+=+56+
(2) +-10a+-+5b+=+-40+
-------------------------
+8a+=+16+
+a+=+2+
and
(2) +2a+%2B+b+=+8+
(2) +2%2A2+%2B+b+=+8+
(2) +b+=+4+
--------------------
flour is $2/kg
sugar is $4/kg
--------------------
check:
(1) +3.6a+%2B+1%2Ab+=+11.2+
(1) +3.6%2A2+%2B+1%2A4+=+11.2+
(1) +7.2+%2B+4+=+11.2+
(1) +11.2+=+11.2+
You can check (2)