SOLUTION: A merchant mixed 10 lb of a cinnamon tea with 4 lb of spice tea. The 14-pound mixture cost $37. A second mixture included 16 lb of the cinnamon tea and 4 lb of the spice tea. The 2

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Question 1140809: A merchant mixed 10 lb of a cinnamon tea with 4 lb of spice tea. The 14-pound mixture cost $37. A second mixture included 16 lb of the cinnamon tea and 4 lb of the spice tea. The 20-pound mixture cost $52. Find the cost per pound of the cinnamon tea and of the spice tea
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
c dollars per pound, cinnamon tea
x dollars per pouns, spice tea


This is already described in a way to allow quick elimination of x to find c.

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

            This problem is to be solved mentally.


An attentive reader will notice momentarily from the condition, that the difference in costs  $52 - $37 = $15  

is exactly the cost of  16 lb - 10 lb = 6 lb of the cinnamon tea.



So the price of the cinnamon tea is   = 2.50 dollars per pound.



Then the cost of 4 lb of the spice tea is  37 - 10*2.5 = 37 - 25 = 12 dollars;

hence, the price of the of the spice tea is  12/4 = 3 dollars per pound.



ANSWER.  $2.50 per pound for the cinnamon tea and $3.00 per pound for the spice tea.

Solved.

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The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


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Free of charge online textbook in ALGEBRA-I
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