Question

Teas costing $7 per pound are to be mixed with teas costing $4 per pound to make a 30-pound mixture. If the mixture is to sell for $6 per pound, how many pounds of each kind of tea should be used?

A) 12 lb at $7/lb, 18 lb at $4/lb
B) 15 lb at $7/lb, 15 lb at $4/lb
C) 20 lb at $7/lb, 10 lb at $4/lb
D) None of the above

Answer 1

To determine how many pounds of each kind of tea to use, set up a system of equations based on the total weight and cost. Solving the system reveals that 20 pounds of $7 tea and 10 pounds of $4 tea are required, which matches option C.

Step-by-step explanation:

To solve the problem of what amounts of teas costing $7 per pound and $4 per pound to mix in order to get a 30-pound mixture that sells for $6 per pound, we can set up a system of equations. Let's call the number of pounds of the $7 tea x and the number of pounds of the $4 tea y.

Since the total weight of the tea mixture is 30 pounds, we have the equation:

• 
  
• x + y = 30

The total cost of x pounds of $7 tea and y pounds of $4 tea should equal the total cost for 30 pounds of $6 tea:

• 
  
• 7x + 4y = 6(30)

To find the values of x and y, we can solve this system of equations. Multiply the first equation by 4 to get:

• 
  
• 4x + 4y = 120

Subtract this from the second equation to get:

• 
  
• 3x = 60

Solve for x to get:

• 
  
• x = 20

Substitute x = 20 into the first equation to get :

• 
  
• 20 + y = 30
• 
  
• y = 10

So, 20 pounds of the $7 tea and 10 pounds of the $4 tea are needed, which corresponds to option C).