A merchant blends tea that sells for $5.45 a pound with tea that sells for $2.45 a pound to produce 80 lb of a mixture that sells for $3.95 a pound. How many pounds of each type of tea does the merchant use in the blend?

lb (at $5.45/lb)
lb (at $2.45/lb)

ET is lbs of expensive tea

CT is cheap tea.

ET*5.45+CT*2.45=(80)3.95

but ET=(80-CT)
put that into the equation for ET, solve for CT. THen solve for ET

To solve this problem, we can set up a system of equations based on the information given.

Let's call the number of pounds of tea that sells for $5.45 per pound "x" and the number of pounds of tea that sells for $2.45 per pound "y".

From the problem, we know that:
1) x + y = 80 (since the total weight of the mixture is 80 lb)
2) (5.45 * x) + (2.45 * y) = 3.95 * 80 (since the total cost of the mixture is the cost per pound multiplied by the weight)

Now we can solve this system of equations.

First, we can solve equation (1) for x:
x = 80 - y

Next, we substitute this expression for x in equation (2):
(5.45 * (80-y)) + (2.45 * y) = 3.95 * 80

Now we can simplify and solve for y:

436 - 5.45y + 2.45y = 316

Combining like terms:

-3y = -120

Divide both sides by -3:

y = 40

Now we can substitute this value of y back into equation (1) to solve for x:

x + 40 = 80

Subtracting 40 from both sides:

x = 40

So, the merchant uses 40 pounds of tea that sells for $5.45 per pound and 40 pounds of tea that sells for $2.45 per pound to produce the 80-pound mixture.