A special tea is a mixture of three kinds of tea leaves A, B and C in the ratio 5 : 3 : 2.1 kg of each kind of tea leaves costs $4, $20 and $10 respectively. What is the cost of 15 kg of this special tea?
Trying to make sense of your typo
I think you meant your ratio was 5:3:2
and then: 1 kg of each kind .....
(looks like the ratio is 5:3:2.1, but then the next part of the sentence
makes no sense)
I read it this way:
ratio of tea mixture:
A:B:C = 5:3:2 = 5x : 3x : 2x
let's assume that we have 1 kg, that is,
9x = 1
x = 1/9
so we have 5/9 kg of A, 3/9 kg of B, and 2/9 kg of C
cost of 1 kg = (5/9)(4) + (3/9)(20) + 2/9(10) dollars
= $(20+60+20)/9
= $100/9
So 15 kg would cost 15(100/9) or $166.67
5+3+2 = 10 parts of tea
so to make 15 kg of the mix, you will need 3/2 as much of each part. That is,
7.5 + 4.5 + 3 kg of each
Then the cost will be
7.5*4 + 4.5*20 + 3*10 = $150
To find the cost of 15 kg of the special tea, we need to determine the cost per kilogram of the tea.
The total ratio of the three types of tea leaves is 5:3:2, which adds up to 10 parts.
To find the cost per kilogram, we divide the total cost by the total weight of the tea leaves:
Total cost = (5 * $4) + (3 * $20) + (2 * $10) = $118
Total weight = 5 + 3 + 2 = 10 kg
Cost per kilogram = $118 / 10 kg = $11.80/kg
Finally, to find the cost of 15 kg of the special tea, we multiply the cost per kilogram by the weight:
Cost of 15 kg of special tea = $11.80/kg * 15 kg = $177
To find the cost of 15 kg of the special tea, we first need to calculate the cost per kilogram of each type of tea leaf.
Let's start by calculating the cost per kilogram of each type of tea leaf:
1) Tea leaves A: The cost of 1 kg of tea leaves A is $4.
2) Tea leaves B: The cost of 1 kg of tea leaves B is $20.
3) Tea leaves C: The cost of 1 kg of tea leaves C is $10.
Next, we need to calculate the total weight of the special tea. The ratio given is 5:3:2, which adds up to 10 parts. This means that for every 10 kg of the special tea, it contains 5 kg of tea leaves A, 3 kg of tea leaves B, and 2 kg of tea leaves C.
To calculate the cost of the special tea, we need to find the cost per kilogram of the mixture. We can do this by finding the weighted average cost across the three types of tea leaves.
Weighted average cost = (Cost of tea leaves A * Weight of tea leaves A + Cost of tea leaves B * Weight of tea leaves B + Cost of tea leaves C * Weight of tea leaves C) / Total weight of the special tea
Plugging in the values, we get:
Weighted average cost = (4 * 5 + 20 * 3 + 10 * 2) / (5 + 3 + 2)
Weighted average cost = (20 + 60 + 20) / 10
Weighted average cost = 100 / 10
Weighted average cost = $10.
Therefore, the cost of 1 kg of the special tea is $10.
To find the cost of 15 kg of the special tea, we multiply the cost per kilogram by the weight:
Cost of 15 kg of the special tea = Cost per kilogram * Weight
Cost of 15 kg of the special tea = $10 * 15
Cost of 15 kg of the special tea = $150.
Hence, the cost of 15 kg of the special tea is $150.