Answer:
The mass of the $4.60/lb tea that should be used in the mixture is 10 lb
The mass of the $5.75/lb tea that should be used in the mixture is 8 lb
The mass of the $6.50/lb tea that should be used in the mixture is 2 lb
Step-by-step explanation:
The parameters of the question are;
The worth of the three teas are
Tea A = $4.60/lb
Tea B = $5.75/lb
Tea C = $6.50/lb
The mass of the mixture of the three teas = 20 lb
The worth of the mixture of the three teas = $5.25 per pound = $5.25/lb
The amount of the $4.60 in the mixture = The sum of the amount of the other two teas
Therefore, given that the mass of the mixture = 20 lb, we have in the mixture;
The mass of tea A + The mass of Tea B + The mass of Tea C = 20 lb
The mass of tea A = The mass of Tea B + The mass of Tea C
Therefore;
The mass of tea A + The mass of tea A = 20 lb
2 × The mass of tea A in the mixture = 20 lb
The mass of tea A in the mixture = 20 lb/2 = 10 lb
The mass of tea A in the mixture = 10 lb
The mass of Tea B + The mass of Tea C = The mass of tea A = 10 lb
The mass of Tea B + The mass of Tea C = 10 lb
The mass of Tea B = 10 lb - The mass of Tea C
Where the mass of Tea C in the mixture = x, we have;
The mass of Tea B in the mixture = 10 lb - x
The cost of the 10 lb of tea A = 10 × $4.60 = $46.0
The worth of the tea mixture = 20 × $5.25 = $105
The worth of the remaining 10 lb of the mixture comprising of tea A and tea B is given as follows;
The worth of Tea B + The worth of Tea C in the mixture = $105.00 - $46.00 = $59.00
Therefore, we have;
x lb × $6.50/lb + (10 - x) lb × $5.75/lb = $59.00
x × $6.50 - x × $5.75 + $57.50 = $59.00
x × $0.75 = $59.00 - $57.50 = $1.50
x = $1.50/$0.75 = 2 lb
∴ The mass of Tea C in the mixture = 2 lb
The mass of Tea B in the mixture = 10 lb - x = 10 lb - 2 lb = 8 lb
The mass of Tea B in the mixture = 8 lb
Therefore, since we have;
Tea A = $4.60/lb
Tea B = $5.75/lb
Tea C = $6.50/lb
The mass of tea A in the mixture = 10 lb
The mass of tea B in the mixture = 8 lb
The mass of tea C in the mixture = 2 lb, we find;
The mass of the $4.60/lb tea that should be used in the mixture = 10 lb
The mass of the $5.75/lb tea that should be used in the mixture = 8 lb
The mass of the $6.50/lb tea that should be used in the mixture = 2 lb.
