Subjects algebra

Proportion Problems Cc65C5

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1. State the problem: Find the value of $x$ if $\frac{3}{4} = \frac{x}{8}$.\n\n2. Use the formula for proportions: $\frac{a}{b} = \frac{c}{d} \implies ad = bc$. This means the product of the means equals the product of the extremes.\n\n3. Apply the formula: $3 \times 8 = 4 \times x$.\n\n4. Simplify: $24 = 4x$.\n\n5. Divide both sides by 4 to isolate $x$: $$\frac{24}{\cancel{4}} = \frac{4x}{\cancel{4}} \implies 6 = x.$$\n\n6. Final answer: $x = 6$.\n\n---\n\n1. State the problem: Find the value of $y$ if $\frac{5}{y} = \frac{10}{12}$.\n\n2. Use the formula for proportions: $\frac{a}{b} = \frac{c}{d} \implies ad = bc$.\n\n3. Apply the formula: $5 \times 12 = y \times 10$.\n\n4. Simplify: $60 = 10y$.\n\n5. Divide both sides by 10 to isolate $y$: $$\frac{60}{\cancel{10}} = \frac{10y}{\cancel{10}} \implies 6 = y.$$\n\n6. Final answer: $y = 6$.