Question

ratios & proportions solve the following proportions: 1. $\frac{27}{x} = \frac{15}{4}$ 2. $\frac{x - 10}{2} = \frac{x - 8}{4}$

Explanation:

Step1: Cross-multiply to isolate x

$27 \times 4 = 15x$

Step2: Calculate left-hand side

$108 = 15x$

Step3: Solve for x

$x = \frac{108}{15} = \frac{36}{5}$

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Step1: Cross-multiply the proportion

$4(x-10) = 2(x-8)$

Step2: Expand both sides

$4x - 40 = 2x - 16$

Step3: Isolate x terms

$4x - 2x = 40 - 16$

Step4: Simplify and solve for x

$2x = 24$
$x = 12$

Answer:

1. $x = \frac{36}{5}$ or $7.2$
2. $x = 12$