Final answer:
The correct amounts of each kind of candy that $3 can buy are inversely proportional to the price per kg. Option a) 3/1 kg of $1 candy, 2/3 kg of $1.50 candy, 1.5 kg of $2 candy, and 1/1 kg of $3 candy is the only correct answer because it properly reflects the inverse relationship between price and quantity.
Step-by-step explanation:
The question requires an understanding of the concept of inverse proportions, where one value decreases as another value increases. In this case, the amount of candy that can be purchased for $3 is inversely proportional to the price per kilogram. If the candy costs more per kg, you can buy less of it with $3, and vice versa. The correct amounts of candy for each price per kg that $3 can buy are calculated by dividing the total amount of money ($3) by the cost per kilogram of each kind of candy.
- $1 candy: $3 ÷ $1/kg = 3/1 kg
- $1.50 candy: $3 ÷ $1.50/kg = 2 kg
- $2 candy: $3 ÷ $2/kg = 1.5 kg
- $3 candy: $3 ÷ $3/kg = 1 kg
The prices and the amounts are inversely proportional because as the price of candy increases, the quantity that can be bought with a fixed sum of money decreases. Therefore, the only correct option where the amounts correspond to the inverse of the price is option a): 3/1 kg of $1 candy; 2/3 kg of $1.50 candy; 1.5 kg of $2 candy; 1/1 kg of $3 candy.
The other options all have mistakes in the calculations; for example, they may not divide $3 by the correct price per kg to get the quantity that can be bought with $3.