exercises 11-3

solve each proportion.
1. $\frac{5}{4} = \frac{75}{n}$
2. $\frac{a}{36} = \frac{1}{9}$
3. $\frac{2}{3} = \frac{8}{2x}$
4. $\frac{90}{64} = \frac{n}{32}$
5. $\frac{4w - 9}{5} = \frac{u + 3}{3}$
6. $\frac{3a}{7} = \frac{6}{1}$
7. $\frac{x}{35} = \frac{16}{40}$
8. $\frac{6x - 2}{7} = \frac{5x + 7}{8}$
9. $\frac{352}{11} = \frac{w}{0.4}$
10. $\frac{3}{11} = \frac{3n}{126}$
11. $\frac{11}{n} = \frac{77}{14}$
12. $\frac{6}{5w} = \frac{4.8}{9}$
13. six is to 15 as some number $x$ is to 45. set up a proportion and solve for $x$.
14. the ratio of 10 to 0.5 is the same as the ratio of 40 to some number $x$. what is the value of $x$?

Question

exercises 11-3

solve each proportion.
1. $\frac{5}{4} = \frac{75}{n}$
2. $\frac{a}{36} = \frac{1}{9}$
3. $\frac{2}{3} = \frac{8}{2x}$
4. $\frac{90}{64} = \frac{n}{32}$
5. $\frac{4w - 9}{5} = \frac{u + 3}{3}$
6. $\frac{3a}{7} = \frac{6}{1}$
7. $\frac{x}{35} = \frac{16}{40}$
8. $\frac{6x - 2}{7} = \frac{5x + 7}{8}$
9. $\frac{352}{11} = \frac{w}{0.4}$
10. $\frac{3}{11} = \frac{3n}{126}$
11. $\frac{11}{n} = \frac{77}{14}$
12. $\frac{6}{5w} = \frac{4.8}{9}$
13. six is to 15 as some number $x$ is to 45. set up a proportion and solve for $x$.
14. the ratio of 10 to 0.5 is the same as the ratio of 40 to some number $x$. what is the value of $x$?

Accepted Answer

{ "quality": "clear", "question_count": 14, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Proportional Reasoning", "Linear Equations Solving" ], "new_concepts": [ "Solving Proportions" ], "current_concepts": [ "Proportional Reasoning", "Linear Equations Solving", "Solving Proportions" ] } ## Solve simple proportions (Questions 1-4, 6, 7, 9-12) $$ \begin{aligned} &\text{1. } \frac{5}{4} = \frac{75}{n} \implies 5n = 300 \implies n = 60\ &\text{2. } \frac{a}{36} = \frac{1}{9} \implies 9a = 36 \implies a = 4\ &\text{3. } \frac{2}{3} = \frac{8}{2x} \implies 4x = 24 \implies x = 6\ &\text{4. } \frac{90}{64} = \frac{n}{32} \implies 64n = 2880 \implies n = 45\ &\text{6. } \frac{3a}{7} = \frac{6}{1} \implies 3a = 42 \implies a = 14\ &\text{7. } \frac{x}{35} = \frac{16}{40} \implies 40x = 560 \implies x = 14\ &\text{9. } \frac{352}{11} = \frac{w}{0.4} \implies 32 = \frac{w}{0.4} \implies w = 12.8\ &\text{10. } \frac{3}{14} = \frac{3n}{126} \implies 42n = 378 \implies n = 9\ &\text{11. } \frac{11}{n} = \frac{77}{14} \implies 77n = 154 \implies n = 2\ &\text{12. } \frac{6}{5w} = \frac{4.8}{9} \implies 24w = 54 \implies w = 2.25 \end{aligned} $$ ## Solve multi-step proportions (Questions 5, 8) $$ \begin{aligned} &\text{5. } \frac{4w - 9}{5} = \frac{w + 3}{3} \implies 3(4w - 9) = 5(w + 3) \implies 12w - 27 = 5w + 15 \implies 7w = 42 \implies w = 6\ &\text{8. } \frac{6x - 2}{7} = \frac{5x + 7}{8} \implies 8(6x - 2) = 7(5x + 7) \implies 48x - 16 = 35x + 49 \implies 13x = 65 \implies x = 5 \end{aligned} $$ ## Solve word problem proportions (Questions 13, 14) $$ \begin{aligned} &\text{13. } \frac{6}{15} = \frac{x}{45} \implies 15x = 270 \implies x = 18\ &\text{14. } \frac{10}{0.5} = \frac{40}{x} \implies 10x = 20 \implies x = 2 \end{aligned} $$ | No. | Answer | |---|---| | 1 | $n = 60$ | | 2 | $a = 4$ | | 3 | $x = 6$ | | 4 | $n = 45$ | | 5 | $w = 6$ | | 6 | $a = 14$ | | 7 | $x = 14$ | | 8 | $x = 5$ | | 9 | $w = 12.8$ | | 10 | $n = 9$ | | 11 | $n = 2$ | | 12 | $w = 2.25$ | | 13 | $\frac{6}{15} = \frac{x}{45}; x = 18$ | | 14 | $x = 2$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Proportions" ] }

No.	Answer
2	\(a = 4\)
3	\(x = 6\)
4	\(n = 45\)
5	\(w = 6\)
6	\(a = 14\)
7	\(x = 14\)
8	\(x = 5\)
9	\(w = 12.8\)
10	\(n = 9\)
11	\(n = 2\)
12	\(w = 2.25\)
13	\(\frac{6}{15} = \frac{x}{45}; x = 18\)
14	\(x = 2\)

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QUESTION IMAGE

Question

Explanation:

Solve simple proportions (Questions 1-4, 6, 7, 9-12)

Solve multi-step proportions (Questions 5, 8)

Solve word problem proportions (Questions 13, 14)

Answer: