A merchant blends tea that sells for $4.40 a pound with tea that sells for $2.30 a pound to produce 120 lb of a mixture that sells for $3.00 a pound. How many pounds of each type of tea does the merchant use in the blend?
If there are x lbs of 4.40 tea, then the rest (120-x) is 2.30
So, we need
4.40x + 2.30(120-x) = 3.00(120)
Now just solve for x.
To solve this problem, let's assign variables to the unknown quantities:
Let's say x represents the pounds of tea that sells for $4.40 a pound.
Similarly, let y represents the pounds of tea that sells for $2.30 a pound.
Now, let's set up equations based on the given information:
1) The total weight of the mixture is 120 pounds:
x + y = 120
2) The cost per pound of the mixture is $3.00:
(4.40x + 2.30y) / 120 = 3.00
To solve this system of equations, we'll use the method of substitution:
First, let's solve equation 1) for x:
x = 120 - y
Now, substitute this value of x in equation 2):
(4.40(120-y) + 2.30y) / 120 = 3.00
Expanding the equation:
(528 - 4.40y + 2.30y) / 120 = 3.00
Combining like terms:
(528 - 2.10y) / 120 = 3.00
Now, cross-multiply to eliminate the fraction:
528 - 2.10y = 3.00 * 120
Simplify and solve for y:
528 - 2.10y = 360
Subtract 528 from both sides:
-2.10y = -168
Divide both sides by -2.10:
y = -168 / -2.10
y = 80
Now that we know y = 80, substitute this value back into equation 1) to find x:
x + 80 = 120
x = 120 - 80
x = 40
Therefore, the merchant used 40 pounds of tea that sells for $4.40 a pound, and 80 pounds of tea that sells for $2.30 a pound in the blend.