(show work for every problem.)
express each of the following as a ratio in simplest form.
1. of the 13 journeymen on a jobsite, there are 5 females. what is the ratio of males to females on this job?
2. what is the ratio of 24 volts to 3 volts?
3. in a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels. what is the ratio of nickels to dimes?

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Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Basic Arithmetic Operations", "Ratio Representation", "Ratio Simplification" ], "new_concepts": [], "current_concepts": [ "Basic Arithmetic Operations", "Ratio Representation", "Ratio Simplification" ] } ## Calculate the ratio of males to females $$ \begin{aligned} &\text{Total Journeymen} = 13\ &\text{Females} = 5\ &\text{Males} = 13 - 5 = 8\ &\text{Ratio of males to females} = 8:5 \end{aligned} $$ ## Simplify the ratio of 24 volts to 3 volts $$ \begin{aligned} &\text{Ratio} = \frac{24}{3} = \frac{8}{1}\ &\text{Ratio in simplest form} = 8:1 \end{aligned} $$ ## Calculate the ratio of nickels to dimes $$ \begin{aligned} &\text{Total value} = \$2.35\ &\text{Value of 6 quarters} = 6 \times \$0.25 = \$1.50\ &\text{Value of 5 dimes} = 5 \times \$0.10 = \$0.50\ &\text{Value of 5 pennies} = 5 \times \$0.01 = \$0.05\ &\text{Subtotal value} = \$1.50 + \$0.50 + \$0.05 = \$2.05\ &\text{Value of nickels} = \$2.35 - \$2.05 = \$0.30\ &\text{Number of nickels} = \frac{\$0.30}{\$0.05} = 6\ &\text{Ratio of nickels to dimes} = 6:5 \end{aligned} $$ ## Question 1 $8:5$ ## Question 2 $8:1$ ## Question 3 $6:5$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Ratio Simplification" ] }

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Explanation:

Calculate the ratio of males to females

Simplify the ratio of 24 volts to 3 volts

Calculate the ratio of nickels to dimes

Answer:

Question 1

Question 2

Question 3