german silver is an alloy composed of nickel, zinc, and copper in a $3:4:13$ ratio. how many kilograms of each metal are needed to make $4\text{ kg}$ of this alloy.

answer

$\square\text{ kg of nickel; } \square\text{ kg of zinc; } \square\text{ kg of copper}$

Question

german silver is an alloy composed of nickel, zinc, and copper in a $3:4:13$ ratio. how many kilograms of each metal are needed to make $4\text{ kg}$ of this alloy.

answer

$\square\text{ kg of nickel; } \square\text{ kg of zinc; } \square\text{ kg of copper}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Three-part Ratios", "Alloy Composition" ], "current_concepts": [ "Ratios", "Three-part Ratios", "Alloy Composition" ] } ## Sum the parts of the ratio $$ 3 + 4 + 13 = 20 $$ ## Calculate the multiplier for 4 kg of alloy $$ \text{Multiplier} = \frac{4\text{ kg}}{20} = 0.2\text{ kg per part} $$ ## Multiply each ratio term by the multiplier $$ \begin{aligned} \text{Nickel} &= 3 \times 0.2 = 0.6\text{ kg} \ \text{Zinc} &= 4 \times 0.2 = 0.8\text{ kg} \ \text{Copper} &= 13 \times 0.2 = 2.6\text{ kg} \end{aligned} $$ German Silver is an alloy composed of nickel, zinc, and copper in a 3 : 4 : 13 ratio. How many kilograms of each metal are needed to make 4 kg of this alloy. Answer 0.6 kg of nickel; 0.8 kg of zinc; 2.6 kg of copper { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Ratios and Proportions" ] }

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Question

Explanation:

Sum the parts of the ratio

Calculate the multiplier for 4 kg of alloy

Multiply each ratio term by the multiplier

Answer: