How many liters of a blue dye that cost 1.80 per liter must be mixed with 20 l of anil which costs 2.60 per liter to make a mixture that cost 2.12 per liter
just keep track of all the costs involved:
1.80x + 2.60(20) = 2.12(x+20)
To determine the quantity of blue dye needed, we can use the concept of weighted averages.
Let's assume x liters of blue dye are required.
The cost of the blue dye is $1.80 per liter, and the cost of the anil is $2.60 per liter. We want the mixture to cost $2.12 per liter.
To find the required quantity, we can use the following equation:
1.80x + 2.60(20) = 2.12(x + 20)
Let's solve for x:
1.80x + 52 = 2.12x + 42.4
0.32x = 9.6
x = 9.6 / 0.32
x ≈ 30
Therefore, approximately 30 liters of the blue dye should be mixed with 20 liters of anil to achieve a mixture that costs $2.12 per liter.
To determine the quantity of blue dye needed, we need to set up an equation based on the cost and volume of the mixture. Let's denote the required quantity of blue dye as x liters.
The cost of the blue dye is $1.80 per liter, so the cost of x liters of blue dye would be 1.80x dollars.
The cost of the anil is $2.60 per liter, and since we have 20 liters of anil, the total cost of the anil is 2.60 * 20 = $52.00.
Since we want a mixture that costs $2.12 per liter, the total cost of the mixture can be calculated as follows:
(total cost of blue dye + total cost of anil) / total volume of mixture
For the total volume of the mixture, we would have x liters of blue dye + 20 liters of anil = (x + 20) liters.
Hence, we can write the equation as:
(1.80x + 52) / (x + 20) = 2.12
To solve this equation, we can start by multiplying both sides by (x + 20) to eliminate the denominator:
1.80x + 52 = 2.12(x + 20)
Now, distribute 2.12 on the right side:
1.80x + 52 = 2.12x + 42.40
Next, let's isolate the variable terms:
1.80x - 2.12x = 42.40 - 52
Simplifying:
-0.32x = -9.60
Divide both sides by -0.32 to solve for x:
x = (-9.60) / (-0.32)
Calculating:
x ≈ 30
Therefore, approximately 30 liters of blue dye that costs $1.80 per liter should be mixed with 20 liters of anil that costs $2.60 per liter to make a mixture that costs $2.12 per liter.