exercises 11-4

assume that the variables $x$ and $y$ are directly proportional. determine the missing value in each case.

1. if $x_1 = 5$, $y_1 = 125$, and $y_2 = 25$, determine the value of $x_2$.
2. if $y_1 = 6$, $x_2 = 15$, and $y_2 = 18$, determine the value of $x_1$.
3. if $x_1 = 2$, $y_1 = 16$, and $x_2 = 3.5$, determine the value of $y_2$.
4. if $x_1 = 32$, $y_1 = 80$, and $y_2 = 45$, determine the value of $x_2$.

Question

exercises 11-4

assume that the variables $x$ and $y$ are directly proportional. determine the missing value in each case.

1. if $x_1 = 5$, $y_1 = 125$, and $y_2 = 25$, determine the value of $x_2$.
2. if $y_1 = 6$, $x_2 = 15$, and $y_2 = 18$, determine the value of $x_1$.
3. if $x_1 = 2$, $y_1 = 16$, and $x_2 = 3.5$, determine the value of $y_2$.
4. if $x_1 = 32$, $y_1 = 80$, and $y_2 = 45$, determine the value of $x_2$.

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 proportion relationship $$ \frac{y_1}{x_1} = \frac{y_2}{x_2} \implies y = kx $$ ## Solve for the missing values in each case $$ \begin{aligned} &\text{Case 1: } \frac{125}{5} = \frac{25}{x_2} \implies 25 = \frac{25}{x_2} \implies x_2 = 1\ &\text{Case 2: } \frac{6}{x_1} = \frac{18}{15} \implies \frac{6}{x_1} = \frac{6}{5} \implies x_1 = 5\ &\text{Case 3: } \frac{16}{2} = \frac{y_2}{3.5} \implies 8 = \frac{y_2}{3.5} \implies y_2 = 28\ &\text{Case 4: } \frac{80}{32} = \frac{45}{x_2} \implies \frac{5}{2} = \frac{45}{x_2} \implies 5x_2 = 90 \implies x_2 = 18 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | If $x_1 = 5$, $y_1 = 125$, and $y_2 = 25$, find $x_2$ | $x_2 = 1$ | | 2 | If $y_1 = 6$, $x_2 = 15$, and $y_2 = 18$, find $x_1$ | $x_1 = 5$ | | 3 | If $x_1 = 2$, $y_1 = 16$, and $x_2 = 3.5$, find $y_2$ | $y_2 = 28$ | | 4 | If $x_1 = 32$, $y_1 = 80$, and $y_2 = 45$, find $x_2$ | $x_2 = 18$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Direct Proportion Equations" ] }

No.	Problem	Answer
2	If \(y_1 = 6\), \(x_2 = 15\), and \(y_2 = 18\), find \(x_1\)	\(x_1 = 5\)
3	If \(x_1 = 2\), \(y_1 = 16\), and \(x_2 = 3.5\), find \(y_2\)	\(y_2 = 28\)
4	If \(x_1 = 32\), \(y_1 = 80\), and \(y_2 = 45\), find \(x_2\)	\(x_2 = 18\)

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QUESTION IMAGE

Question

Explanation:

Set up the direct proportion relationship

Solve for the missing values in each case

Answer: