Question

a store sells different kinds of candy at \\$1, \\$1.50, \\$2, and \\$3 per kilogram. how many kilograms of each kind of candy does \\$3 buy? explain why the price of 1 kg and the amount of candy that \\$3 can buy are inversely proportional quantities?

give your explanation on paper.

answer
kg of \\$1 candy; kg of \\$1.50 candy; kg of \\$2 candy; kg of \\$3 candy

Explanation:

Identify the given values

We have a total budget of \( \$3 \).
The prices per kilogram are \( \$1 \), \( \$1.50 \), \( \$2 \), and \( \$3 \).

Set up the relationship

Using the Inverse Proportionality concept, the amount of candy \( q \) in kilograms bought with a fixed budget \( B \) at a price \( p \) per kilogram is:

$$ q = \frac{B}{p} $$

Here, \( B = 3 \).

Calculate each quantity

Using the Inverse Variation concept, we compute the kilograms for each price:

• For \( \$1 \) candy:

$$ q_1 = \frac{3}{1} = 3\text{ kg} $$

• For \( \$1.50 \) candy:

$$ q_2 = \frac{3}{1.50} = 2\text{ kg} $$

• For \( \$2 \) candy:

$$ q_3 = \frac{3}{2} = 1.5\text{ kg} $$

• For \( \$3 \) candy:

$$ q_4 = \frac{3}{3} = 1\text{ kg} $$

Explain the inverse relationship

The product of the price per kilogram and the quantity purchased is always constant:

$$ p \times q = 3 $$

Since their product is constant, the price and quantity are inversely proportional.

Answer:

A store sells different kinds of candy at $1, $1.50, $2, and $3 per kilogram. How many kilograms of each kind of candy does $3 buy? Explain why the price of 1 kg and the amount of candy that $3 can buy are inversely proportional quantities?

<blank>3</blank> kg of $1 candy; 2 kg of $1.50 candy; <blank>1.5</blank> kg of $2 candy; 1 kg of $3 candy