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26 Dec 2025, 05:29
Kudos
Bookmarks
Price = fraction of compost x total mass
First mixture total mass= 3+4=7
Fractio of compost = 3/7
Second mixture total mass= 6+15= 21
Fraction of compost= 6/21=2/7
Price per kg= P x (fraction of compost)
72/7=p x 3/7
p=24
Price per kg for second mixture= 24x2/7=48/7
Total price of second mixture= 21x48/7= 3x48= 144
Fial answer is 144 cents
First mixture total mass= 3+4=7
Fractio of compost = 3/7
Second mixture total mass= 6+15= 21
Fraction of compost= 6/21=2/7
Price per kg= P x (fraction of compost)
72/7=p x 3/7
p=24
Price per kg for second mixture= 24x2/7=48/7
Total price of second mixture= 21x48/7= 3x48= 144
Fial answer is 144 cents
26 Dec 2025, 05:43
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We know that,
Price per kg directly proportional to fraction of compost in the mixture
Let Compost weight be x and Manure weight be y
=> Price = k * x/x + y
We are given,
x = 3kg
y = 4kg
Total mass = 7kg
Total price = 72
=> Price per kg = 72/7
=> 72/7 = k * 3/7
=> k = 24
We need to know price for the second mixture
Compost = 6kg
Manure = 15kg
Total mass = 21kg
Price per kg = k* (6/15+6) = 24 *2/7 = 48/7
Therefore,
Total price = 21*48/7 = 144
B. 144 cents
Price per kg directly proportional to fraction of compost in the mixture
Let Compost weight be x and Manure weight be y
=> Price = k * x/x + y
We are given,
x = 3kg
y = 4kg
Total mass = 7kg
Total price = 72
=> Price per kg = 72/7
=> 72/7 = k * 3/7
=> k = 24
We need to know price for the second mixture
Compost = 6kg
Manure = 15kg
Total mass = 21kg
Price per kg = k* (6/15+6) = 24 *2/7 = 48/7
Therefore,
Total price = 21*48/7 = 144
B. 144 cents
msignatius
26 Dec 2025, 05:55
Kudos
Bookmarks
The tricky part is to understand what is meant by "price per kilogram of the mixture is directly proportional to the fraction of compost"
Another way to read this is, "the higher the amount of compost in the mixture, the higher its price per kilogram."
You can imagine it to be like the purity index of gold - the more its carat (24 vs 22), the more real gold in the mix.
So, what this statement essentially proves is - the percentage of compost in the mixture will define its price (and the amount of other the other compound in the mix - here manure - will help us evaluate this proportion).
Now, if it states we have a mixture with 3KGs of compost and 4KGs of manure, then it means that in this total mixture of 7KGs, 3 / 7 is the compost, and that ratio drives the price up to 72 cents.
Now, if we instead take a mixture of 6 kilograms of compost with 15 kilograms of manure, the proportion changes from 3 / 7 to 6KG compost in (6 + 15) = 21KGs total mixture; or a 6:21 ratio, that's 2 to 7. Hence, if the original mixture had this proportion, a 7KG mixture would contain 2KGs of manure to 7KGs of the total mixture. This was also DIRECTLY impact the price - from 72 cents to 72 / 3 = 24*2 = 48 cents.
Now that the ratios are identical, we can find out the price of from, 2KGs of Compost to 5KGs Manure (or 48 cents), by multiplying it by 3 to arrive at 6KG of Compost + 15KG of Manure = 48*3 = 144 cents or Answer B.
Another way to read this is, "the higher the amount of compost in the mixture, the higher its price per kilogram."
You can imagine it to be like the purity index of gold - the more its carat (24 vs 22), the more real gold in the mix.
So, what this statement essentially proves is - the percentage of compost in the mixture will define its price (and the amount of other the other compound in the mix - here manure - will help us evaluate this proportion).
Now, if it states we have a mixture with 3KGs of compost and 4KGs of manure, then it means that in this total mixture of 7KGs, 3 / 7 is the compost, and that ratio drives the price up to 72 cents.
Now, if we instead take a mixture of 6 kilograms of compost with 15 kilograms of manure, the proportion changes from 3 / 7 to 6KG compost in (6 + 15) = 21KGs total mixture; or a 6:21 ratio, that's 2 to 7. Hence, if the original mixture had this proportion, a 7KG mixture would contain 2KGs of manure to 7KGs of the total mixture. This was also DIRECTLY impact the price - from 72 cents to 72 / 3 = 24*2 = 48 cents.
Now that the ratios are identical, we can find out the price of from, 2KGs of Compost to 5KGs Manure (or 48 cents), by multiplying it by 3 to arrive at 6KG of Compost + 15KG of Manure = 48*3 = 144 cents or Answer B.
Bunuel
