5. if $x_1 = 45$, $x_2 = 0.5$, and $y_2 = 2$, determine the value of $y_1$.
6. if $x_1 = \$11.00$, $y_1 = 2$, and $y_2 = 3$, determine the value of $x_2$.
7. if $y_1 = 560$, $x_2 = 5$, and $y_2 = 100$, determine the value of $x_1$.
8. if $x_1 = 1$, $y_1 = 120$, and $x_2 = 1.75$, determine the value of $y_2$.

Question

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Direct Proportion Equations", "Solving Proportions" ], "new_concepts": [], "current_concepts": [ "Direct Proportion Equations", "Solving Proportions" ] } ## Set up the direct variation relationship $$ \frac{y_1}{x_1} = \frac{y_2}{x_2} \implies y_1 x_2 = y_2 x_1 $$ ## Solve each question using the proportion formula $$ \begin{aligned} &\text{Question 5: } y_1 = \frac{y_2 x_1}{x_2} = \frac{2 \cdot 45}{0.5} = 180\ &\text{Question 6: } x_2 = \frac{y_2 x_1}{y_1} = \frac{3 \cdot 11.00}{2} = 16.50\ &\text{Question 7: } x_1 = \frac{y_1 x_2}{y_2} = \frac{560 \cdot 5}{100} = 28\ &\text{Question 8: } y_2 = \frac{y_1 x_2}{x_1} = \frac{120 \cdot 1.75}{1} = 210 \end{aligned} $$ | No. | Answer | |---|---| | 5 | $y_1 = 180$ | | 6 | $x_2 = \$16.50$ | | 7 | $x_1 = 28$ | | 8 | $y_2 = 210$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Direct Proportion Equations" ] }

No.	Answer
6	\(x_2 = \$16.50\)
7	\(x_1 = 28\)
8	\(y_2 = 210\)

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QUESTION IMAGE

Question

Explanation:

Set up the direct variation relationship

Solve each question using the proportion formula

Answer: