Find the cost per pound of the cinnamon tea and of the spice tea.

Question

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 14 lb of the cinnamon tea and 12 lb of the spice tea. The 26-pound mixture cost $71. Find the cost per pound of the cinnamon tea and of the spice tea.
cinnamon           dollars per pound
spice                  dollars per pound

Answer 1

14 lb mixture costs $37 10 lb cinnamon & 4 lb spice'

26 lb mixture costs $71, 14 lb cinnamon and 12 lb spice

how much does cinnamon cost per pound? spice per pound??

10x + 4y = 14(37) x= cinnamon cost, y=spice cost

14x +12y = 26(71)

30x +12y = 42(37)

subtract to eliminate y

16x = 42(37)-26(71)= -

x=-292/16 =-73/4 = -$18.25 per pound for cinnamon, a negative "price"

y = (14(37)-10(18.25))/4 = (518+182.5)/4 = 175125

= $175.13 per pound for spice

there's a problem with the problem. it's set up so that cinnamon will have a negative price. which makes no seense