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

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

give your explanation on paper.

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Inverse Variation", "Inverse Proportionality" ], "new_concepts": [], "current_concepts": [ "Inverse Variation", "Inverse Proportionality", "Proportions" ] } ## Calculate the amount of each candy Using the *Inverse Proportionality* and *Inverse Variation* knowledge points $$ \begin{aligned} &\text{Amount of } \$1 \text{ candy} = \frac{\$3}{\$1/\text{kg}} = 3\text{ kg} \ &\text{Amount of } \$1.50 \text{ candy} = \frac{\$3}{\$1.50/\text{kg}} = 2\text{ kg} \ &\text{Amount of } \$2 \text{ candy} = \frac{\$3}{\$2/\text{kg}} = 1.5\text{ kg} \ &\text{Amount of } \$3 \text{ candy} = \frac{\$3}{\$3/\text{kg}} = 1\text{ kg} \end{aligned} $$ ## Explain the inverse relationship Using the *Inverse Proportionality* and *Inverse Variation* knowledge points $$ \begin{aligned} &\text{Price per kg } (p) \times \text{Amount in kg } (a) = \text{Total Cost } (\$3) \ &p \cdot a = 3 \implies a = \frac{3}{p} \end{aligned} $$ Since their product is a constant value of $3$, the quantities are inversely proportional. 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? 3 kg of \$1 candy; 2 kg of \$1.50 candy; 1.5 kg of \$2 candy; 1 kg of \$3 candy { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Variation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the amount of each candy

Explain the inverse relationship

Answer: