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A gardener mixes compost and manure to sell in the market. The price per kilogram of the mixture is directly proportional to the fraction (by mass) of compost in the mixture. The gardener sells a mixture containing 3 kilograms of compost and 4 kilograms of manure for 72 cents. How much will the gardener sell a mixture containing 6 kilograms of compost and 15 kilograms of manure for?
A. 96 cents
B. 144 cents
C. 216 cents
D. 270 cents
E. 288 cents
A. 96 cents
B. 144 cents
C. 216 cents
D. 270 cents
E. 288 cents
12 Jan 2026, 11:57
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Official Solution:
A gardener mixes compost and manure to sell in the market. The price per kilogram of the mixture is directly proportional to the fraction (by mass) of compost in the mixture. The gardener sells a mixture containing 3 kilograms of compost and 4 kilograms of manure for 72 cents. How much will the gardener sell a mixture containing 6 kilograms of compost and 15 kilograms of manure for?
A. 96 cents
B. 144 cents
C. 216 cents
D. 270 cents
E. 288 cents
Notice that we are told that the price per kilogram is directly proportional to the fraction (by mass) of compost in the mixture. This means:
1 kg of mixture = \(k\) * (compost weight)/(compost weight + manure weight)
Therefore, for a mixture weighing \(c + m\) kilograms, the price will be:
\((k * \frac{c}{c + m}) * {(c + m)} = kc\)
This shows that the cost of the mixture depends solely on the amount of compost in it. So, if 3 kilograms of compost and 4 kilograms of manure are sold for 72 cents, then a mixture with 6 kilograms of compost and 15 kilograms of manure will be sold for twice as much, which is 144 cents.
Answer: B
A gardener mixes compost and manure to sell in the market. The price per kilogram of the mixture is directly proportional to the fraction (by mass) of compost in the mixture. The gardener sells a mixture containing 3 kilograms of compost and 4 kilograms of manure for 72 cents. How much will the gardener sell a mixture containing 6 kilograms of compost and 15 kilograms of manure for?
A. 96 cents
B. 144 cents
C. 216 cents
D. 270 cents
E. 288 cents
Notice that we are told that the price per kilogram is directly proportional to the fraction (by mass) of compost in the mixture. This means:
1 kg of mixture = \(k\) * (compost weight)/(compost weight + manure weight)
Therefore, for a mixture weighing \(c + m\) kilograms, the price will be:
\((k * \frac{c}{c + m}) * {(c + m)} = kc\)
This shows that the cost of the mixture depends solely on the amount of compost in it. So, if 3 kilograms of compost and 4 kilograms of manure are sold for 72 cents, then a mixture with 6 kilograms of compost and 15 kilograms of manure will be sold for twice as much, which is 144 cents.
Answer: B
