Assess which explanation on how to obtain the value of x in the equation 4x=3681 is reasonable.(1 point)

Question

Responses

Multiply the numerators and denominators. Equate the product to calculate the value of x.
Multiply the numerators and denominators. Equate the product to calculate the value of x .

Reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.
Reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.

Divide 81 by 9 to obtain the value of x.
Divide 81 by 9 to obtain the value of x .

Divide 36 by 81, and then multiply by 4 to determine the value of x.
Divide 36 by 81, and then multiply by 4 to determine the value of x .

Answer 1

To solve the equation \( 4x = 3681 \), we can isolate \( x \) by dividing both sides of the equation by 4:

\[ x = \frac{3681}{4} \]

Now, let's assess the explanations given:

1. Multiply the numerators and denominators. Equate the product to calculate the value of x.

   • This explanation is not relevant to the equation and does not correctly describe the solution process.

2. Reduce the second ratio by dividing both numbers by 9, and then multiplying the result by 4.

   • This explanation does not apply to the equation \( 4x = 3681 \) and is not a reasonable method to find \( x \).

3. Divide 81 by 9 to obtain the value of x.

   • This explanation is incorrect because it does not correspond to the equation we are trying to solve.

4. Divide 36 by 81, and then multiply by 4 to determine the value of x.

   • This explanation is also incorrect and does not relate to the equation \( 4x = 3681 \).

None of the explanations provided are reasonable or applicable to solving the equation \( 4x = 3681 \). The correct approach is to divide \( 3681 \) by \( 4 \) to find \( x \). The result of that division is:

\[ x = 920.25 \]