linear equations with two variables word problem

Question

A merchant mixes 4 lbs of cinnamon tea with 1 lb of spice tea to create a mixture that costs $12 per pound. When the merchant mixes 1 lb of the cinnamon tea with 4 lb of the spice tea, the mixture costs $15 per pound. Is the cost per pound of the cinnamon tea less than equal to, or greater than the cost per pound of the spice tea?

Answer 1

4x + 1y = 12*5 = 60

 

y = 60 - 4x <--- this is the 1st equation

 

 

x + 4y = 15*5 = 75 <--- this is the 2nd equation

 

x + 4(60-4x) = 75 <--- substitutes 1st equation

x + 240 - 16x = 75

 

-15x + 240  = 75

 

-15x = 75-240

 

-15x = -165

 

x=11

 

The cinnamon tea costs $11 per pound

The spice tea, per 1st equation,costs 60 - 4(11) = $16 per pound

 

Answer 2

4c + 1s = 5(12) = 60

 

1c + 4s = 5(15) = 75, c = 75 - 4s

 

Substitute:

 

4(75 - 4s) + s = 60

 

300 - 16s + s = 60

 

15s = 240

 

s = 16, this is the price of the spice tea

 

c = 75 - 4s

 

c = 75 - 4(16)

 

c = 75 - 64 = 11, this is the price of the cinnamon tea