Final answer:
To make 10 pounds of tea that is 17.1% jasmine, 3 pounds of the 22% jasmine tea are needed, with the remainder being the 15% jasmine tea. The calculation involves setting up an equation and solving for the unknown amount using decimal percentages.
Step-by-step explanation:
To calculate how many pounds of 22% jasmine tea are used to make 10 lb of tea that is 17.1% jasmine, we can use the method of mixtures and percent concentrations. Let's denote the amount of 22% jasmine tea as x pounds, hence the amount of 15% jasmine tea will be 10 - x pounds.
Now, we can set up the equation based on the concentration of jasmine in each tea:
(22% × x) + (15% × (10 - x)) = 17.1% × 10
Convert the percentages to decimals and solve for x:
(0.22 × x) + (0.15 × (10 - x)) = 1.71
Distributing and combining like terms, we get:
0.22x + 1.5 - 0.15x = 1.71
0.07x = 0.21
Dividing by 0.07 on both sides to solve for x:
x = 3
Therefore, 3 pounds of the 22% jasmine tea are needed to create the desired blend.