A grocer has two types of tea. One sells for 8$ per pound, and the other sells for 6$ per pound. How many pounds of each kind must he use to make 50 pounds of tea that will sell for 7.40 per pound
Let x be the number of pounds of the first type of tea (priced at 8$ per pound) and y be the number of pounds of the second type of tea (priced at 6$ per pound).
We know that the total weight of the mixture is 50 pounds, so x + y = 50.
We also know that the average price of the mixture is 7.40 per pound, so the total cost of the mixture is 7.40 * 50 = 370$.
We can set up a system of equations to solve for x and y:
8x + 6y = 370
x + y = 50
Now we can solve this system of equations. Multiplying the second equation by 6, we get:
6x + 6y = 300
Subtracting the second equation from the first, we get:
2x = 70
x = 35
Substitute x back into the second equation:
35 + y = 50
y = 15
So, the grocer must use 35 pounds of the 8$ per pound tea and 15 pounds of the 6$ per pound tea to make 50 pounds of tea that will sell for 7.40 per pound.