black tea at $2.40 per kg is mixed with green tea at $3.20 per kg in the ratio 1:3 calculate the weight of each type of tea in 40 kg of the mixture and calculate the price per kg of the mixture
clearly the black tea is 1/4 of the total
The price p is thus
10(2.40)+30(3.20) = 40p
Well, well, well... Looks like we have a tea party going on here! Let's get brewing with some math and humor.
First, since the ratio of black tea to green tea is 1:3, we can say that for every 1 part of black tea, there are 3 parts of green tea.
Now, let's calculate the weight of each type of tea in the mixture. Since we have a total of 40 kg, we can divide it by 1+3 = 4 (1 part black tea + 3 parts green tea).
Weight of black tea = (1/4) * 40 kg = 10 kg
Weight of green tea = (3/4) * 40 kg = 30 kg
So, we have 10 kg of black tea and 30 kg of green tea swimming in our tea party mixture!
Next, let's calculate the price per kg of the mixture. We'll have to consider the prices of both teas as well as their respective quantities.
The total cost of black tea = 10 kg * $2.40/kg = $24
The total cost of green tea = 30 kg * $3.20/kg = $96
The total cost of the mixture = $24 + $96 = $120
Since the total weight of the mixture is 40 kg, we can now calculate the price per kg.
Price per kg of the mixture = Total cost of mixture / Total weight of mixture
= $120 / 40 kg
= $3 per kg
So, my dear tea party enthusiasts, the price per kg of this delightful mixture is $3. Sip it up, enjoy, and raise your cups to the perfect blend of humor and mathematics!
Let's start by calculating the weight of each type of tea in 40 kg of the mixture.
Given that the ratio of black tea to green tea is 1:3, we can represent the weight of black tea as x and the weight of green tea as 3x.
The total weight of the mixture is 40 kg, so:
x + 3x = 40 kg
4x = 40 kg
x = 40 kg / 4
x = 10 kg
Therefore, there are 10 kg of black tea and 3 times that amount, or 30 kg, of green tea in the mixture.
Next, let's calculate the price per kg of the mixture.
The total cost of the black tea is the weight (10 kg) multiplied by the cost per kg ($2.40):
Cost of black tea = 10 kg × $2.40/kg = $24
The total cost of the green tea is the weight (30 kg) multiplied by the cost per kg ($3.20):
Cost of green tea = 30 kg × $3.20/kg = $96
The total cost of the mixture is the sum of the costs of the black tea and green tea:
Total cost of mixture = $24 + $96 = $120
The total weight of the mixture is 40 kg, so the price per kg of the mixture is:
Price per kg of mixture = Total cost of mixture / Total weight of mixture
Price per kg of mixture = $120 / 40 kg
Price per kg of mixture = $3/kg
Therefore, the weight of black tea in the mixture is 10 kg, the weight of green tea is 30 kg, and the price per kg of the mixture is $3.
To calculate the weight of each type of tea in 40 kg of the mixture, we first need to determine the amount of each tea based on the given ratio.
Let's assume the weight of black tea is x kg, and the weight of green tea is 3x kg (as the ratio of black tea to green tea is 1:3).
According to the given information, the total weight of the mixture is 40 kg:
x + 3x = 40
4x = 40
x = 10
Therefore, the weight of black tea in the mixture is 10 kg, and the weight of green tea is 3 * 10 = 30 kg.
To calculate the price per kg of the mixture, we need to determine the total cost of the mixture and then divide it by the total weight.
The cost of the black tea is $2.40 per kg, and the cost of the green tea is $3.20 per kg.
The total cost of the black tea in 10 kg is 10 * $2.40 = $24.
The total cost of the green tea in 30 kg is 30 * $3.20 = $96.
The total cost of the mixture is $24 + $96 = $120.
The total weight of the mixture is 40 kg.
Therefore, the price per kg of the mixture is $120 divided by 40 kg, which equals $3.00 per kg.
So, in 40 kg of the mixture, there are 10 kg of black tea, 30 kg of green tea, and the price per kg of the mixture is $3.00.