SOLUTION: A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea. The 15 pd mixture cost $40. A second mixture included 12 lb of the cinnamon tea and 8 lb of the spice tea. The 20 pd
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Question 198299This question is from textbook Intermediate Algebra An Applied Approach
: A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea. The 15 pd mixture cost $40. A second mixture included 12 lb of the cinnamon tea and 8 lb of the spice tea. The 20 pd mixture cost $54. Find the cost per pound of the cinnamon tea and of the spice tea.
This question is from textbook Intermediate Algebra An Applied Approach
Found 2 solutions by arallie, ankor@dixie-net.com:
Answer by arallie(162) (Show Source): You can put this solution on YOUR website!
Make an algebra problem
Solve for a variable and substitute
--->
Substitute
Check
cost per pound of the cinnamon tea $2.50
and of the spice tea $3.00
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea.
The 15 pd mixture cost $40.
:
A second mixture included 12 lb of the cinnamon tea and 8 lb of the spice tea.
:
The 20 pd mixture cost $54. Find the cost per pound of the cinnamon tea and of the spice tea.
:
Let c = cost/lb for cinnamon tea
Let s = cost/lb for spice tea
:
Two equations
10c + 5s = 40
12c + 8s = 54
:
Multiply 1st equation by 8, the 2nd equation by 5, results:
80c + 40s = 320
60c + 40s = 270
-------------------subtraction eliminates s, find c
20c = 50
c =
c = $2.50 a lb for cinnamon tea
:
Find s, substitute 2.5 for c in the 1st equation
25 + 5s = 40
5s = 40 - 25
s =
s = $3 for spice tea
;
;
Check solution 2nd equation
12(2.5) + 8(3) =
30 + 24 = 54
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