Question

Describe two different ways to solve 5/6 = x/24 and demonstrate both methods.

Answer 1

The solution to the equation
`\( (5)/(6) = (x)/(24) \) is \( x = 20 \)`.

Explanation:

One way to solve the equation
`\( (5)/(6) = (x)/(24) \)` is by cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction. Solving this equation yields
`\( x = 20 \).`

Another approach is to recognize the proportionality between the fractions. By multiplying both sides of the equation by the common denominator, 24, you eliminate the denominators and simplify the equation to
`\( 24 * (5)/(6) = x \)`. The result,
`\( x = 20 \)`, confirms the solution.

In summary, both methods—cross-multiplication and multiplying by the common denominator—lead to the same solution, demonstrating the flexibility of these approaches in solving proportionality equations. The value of
`\( x = 20 \)` satisfies the given proportion and establishes the relationship between the two fractions.