SOLUTION: 5 Kg of tea and 8 Kg of coffee cost $58. The price of tea increases by 15% and that of coffee by 10%. The new total is $65.30. What are the new prices for 1 Kg of tea and 1 Kg of c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 5 Kg of tea and 8 Kg of coffee cost $58. The price of tea increases by 15% and that of coffee by 10%. The new total is $65.30. What are the new prices for 1 Kg of tea and 1 Kg of c      Log On


   

Question 133520: 5 Kg of tea and 8 Kg of coffee cost $58. The price of tea increases by 15% and that of coffee by 10%. The new total is $65.30. What are the new prices for 1 Kg of tea and 1 Kg of coffee?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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5 Kg of tea and 8 Kg of coffee cost $58. The price of tea increases by 15% and that of coffee by 10%. The new total is $65.30. What are the new prices for 1 Kg of tea and 1 Kg of coffee?
:
Let x = original price of tea
Let y = original price of coffee:
:
Write two equations:
:
Original cost equation:
5x + 8y = 58
5x = 58 - 8y
x = %28%2858-8y%29%29%2F5
:
New cost equation:
5(1.15x) + 8(1.1y) = 65.30
5.75x + 8.8y = 65.30
:
Replace x in the above equation with %28%2858-8y%29%29%2F5
5.75%28%2858-8y%29%29%2F5 + 8.8y = 65.30
Cancel 5 into 5.75
1.15(58-8y) + 8.8y = 65.30
66.7 - 9.2y + 8.8y = 65.30
-9.2y + 8.8y = 65.30 - 66.7
-.4y = -1.4
y = $3.50 original cost of the coffee
:
Then: 1.1 * 3.50 = $3.85 new cost of the coffee
:
:
Find original cost of the tea
5x + 8(3.5) = 58
5x + 28 = 58
5x = 58 - 28
x = 30/5
x = $6.00 original cost of the tea
:
Then: 1.15 * 6 = $6.90 new cost of the tea
:
:
Check solutions by finding the new total
5(6.9) + 8(3.85) =
34.5 + 30.8 = 65.30 confirms our solutions