How many pounds of $1.60 tea must be added to tea costing $1.80 per pound to make a new mixture of 100 pounds costing $1.75 per pound?
(t * 1.6) + [(100 - t) * 1.8) = 100 * 1.75
solve for t
To find out how many pounds of $1.60 tea must be added, we can use the method of mixture problems.
Let's assume the number of pounds of $1.60 tea to be added is 'x' pounds.
The total cost of the $1.60 tea would then be 1.6x dollars.
We know that the total weight of the new mixture will be 100 pounds, so the weight of the $1.80 tea will be (100 - x) pounds.
The total cost of the $1.80 tea would be (1.8 * (100 - x)) dollars.
To get the final mixture costing $1.75 per pound, the total cost of both teas combined should be equal to the cost per pound multiplied by the total weight. Therefore, we have:
1.6x + 1.8 * (100 - x) = 1.75 * 100
To solve this equation, we can simplify and rearrange:
1.6x + 180 - 1.8x = 175
0.2x = 5
x = 5 / 0.2
x = 25
So, 25 pounds of $1.60 tea must be added to tea costing $1.80 per pound to make a new mixture of 100 pounds costing $1.75 per pound.