A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28.
A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37.
Find the cost per pound of the cinnamon tea and of the spice tea.
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12x + 5y = 28 dollars (1)
14x + 8y = 37 dollars (2)
Multiply equation (1) by 8 (both sides).
Multiply equation (2) by 5 (both sides). You will get
96x + 40y = 28*8 (3)
70x + 40y = 37*5 (4)
From equation (3), subtract equation (4). You will get
26x = 28*8 - 37*5 = 39
x = 39/26 = = 1.50 dollars.
To find y, substitute the found value x= 1.50 into equation (1). You will get
12*1.50 + 5y = 28
18 + 5y = 28
5y = 28-18 = 10
y = 10/2 = 5.
ANSWER. Cinamon tea price is $1.50 per pound. The spice tea price is $2.00 dollars per pound.
Solved.
The method I used in the solution, is called the ELIMINATION method.