Question

kuta software - infinite algebra 1
solving proportions
solve each proportion.

1. \\(\frac{10}{8}=\frac{n}{10}\\)
2. \\(\frac{7}{5}=\frac{x}{3}\\)
3. \\(\frac{9}{6}=\frac{x}{10}\\)
4. \\(\frac{7}{n}=\frac{8}{7}\\)
5. \\(\frac{4}{3}=\frac{8}{x}\\)
6. \\(\frac{7}{b + 5}=\frac{10}{5}\\)
7. \\(\frac{6}{b - 1}=\frac{9}{7}\\)
8. \\(\frac{4}{m - 8}=\frac{8}{2}\\)
9. \\(\frac{5}{6}=\frac{7n + 9}{9}\\)
10. \\(\frac{4}{9}=\frac{r - 3}{6}\\)

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Explanation:

Step1: Cross-multiply to isolate $n$

$10 \times 10 = 8n$
$100 = 8n$

Step2: Solve for $n$

$n = \frac{100}{8} = \frac{25}{2}$

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Step1: Cross-multiply to isolate $x$

$7 \times 3 = 5x$
$21 = 5x$

Step2: Solve for $x$

$x = \frac{21}{5}$

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Step1: Cross-multiply to isolate $x$

$9 \times 10 = 6x$
$90 = 6x$

Step2: Solve for $x$

$x = \frac{90}{6} = 15$

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Step1: Cross-multiply to isolate $n$

$7 \times 7 = 8n$
$49 = 8n$

Step2: Solve for $n$

$n = \frac{49}{8}$

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Step1: Cross-multiply to isolate $x$

$4x = 8 \times 3$
$4x = 24$

Step2: Solve for $x$

$x = \frac{24}{4} = 6$

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Step1: Cross-multiply to isolate $b$

$7 \times 5 = 10(b+5)$
$35 = 10b + 50$

Step2: Rearrange and solve for $b$

$10b = 35 - 50 = -15$
$b = \frac{-15}{10} = -\frac{3}{2}$

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Step1: Cross-multiply to isolate $b$

$6 \times 7 = 9(b-1)$
$42 = 9b - 9$

Step2: Rearrange and solve for $b$

$9b = 42 + 9 = 51$
$b = \frac{51}{9} = \frac{17}{3}$

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Step1: Cross-multiply to isolate $m$

$4 \times 2 = 8(m-8)$
$8 = 8m - 64$

Step2: Rearrange and solve for $m$

$8m = 8 + 64 = 72$
$m = \frac{72}{8} = 9$

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Step1: Cross-multiply to isolate $n$

$5 \times 9 = 6(7n+9)$
$45 = 42n + 54$

Step2: Rearrange and solve for $n$

$42n = 45 - 54 = -9$
$n = \frac{-9}{42} = -\frac{3}{14}$

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Step1: Cross-multiply to isolate $r$

$4 \times 6 = 9(r-3)$
$24 = 9r - 27$

Step2: Rearrange and solve for $r$

$9r = 24 + 27 = 51$
$r = \frac{51}{9} = \frac{17}{3}$

Answer:

1. $n = \frac{25}{2}$
2. $x = \frac{21}{5}$
3. $x = 15$
4. $n = \frac{49}{8}$
5. $x = 6$
6. $b = -\frac{3}{2}$
7. $b = \frac{17}{3}$
8. $m = 9$
9. $n = -\frac{3}{14}$
10. $r = \frac{17}{3}$