Final answer:
To create the desired 20-pound tea blend that sells for $2.76 per pound, 8 pounds of the $3.90 tea and 12 pounds of the $2 tea should be mixed together. This is determined by solving a system of linear equations representing the total weight and the total value of the blend.
Step-by-step explanation:
To solve the problem of mixing two grades of tea to get 20 pounds that will sell for $2.76 per pound, we use a system of equations. Let x be the amount of tea worth $3.90 per pound and y be the amount of tea worth $2.00 per pound. We are given two pieces of information that can be transformed into equations:
- The total weight of the tea is 20 pounds: x + y = 20
- The total value of the 20 pounds of tea at $2.76 per pound is $55.20: 3.90x + 2y = 55.20.
Solving these equations simultaneously gives us the amounts of each grade of tea needed. First, solve the first equation for y by subtracting x from 20: y = 20 - x. Substituting this expression for y into the second equation gives 3.90x + 2(20 - x) = 55.20. Simplify and solve for x:
3.90x + 40 - 2x = 55.20
1.90x = 15.20
x = 8
Substitute x = 8 into y = 20 - x to find y:
y = 20 - 8
y = 12
Thus, 8 pounds of the $3.90 tea and 12 pounds of the $2 tea are needed to create the blend.