If $\frac{x}{\sqrt{1.21}}=440$, then x is equal to :

Q: If $\frac{x}{\sqrt{1.21}}=440$, then x is equal to :

To solve the equation $\frac{x}{\sqrt{1.21}} = 440$, we need to find the value of $x$. 1. **Calculate $\sqrt{1.21}$:** \[ \sqrt{1.21} = 1.1 \] This is because $1.1 \times 1.1 = 1.21$. 2. **Substitute $\sqrt{1.21}$ back into the equation:** \[ \frac{x}{1.1} = 440 \] 3. **Solve for $x$:** Multiply both sides of the equation by 1.1 to isolate $x$: \[ x = 440 \times 1.1 \] \[ x = 484 \] Thus, the value of $x$ is 484, which corresponds to Option 1. **Explanation of why other options are incorrect:** - **Option 2 (400):** If $x$ were 400, then substituting back into the equation would give: \[ \frac{400}{1.1} \approx 363.64 \] This does not equal 440, so Option 2 is incorrect. - **Option 3 (532.4):** If $x$ were 532.4, then substituting back into the equation would give: \[ \frac{532.4}{1.1} \approx 484 \] While this calculation seems close, it does not match the original equation setup, which requires $x$ to be exactly 484 when multiplied by 1.1 to equal 440. Therefore, Option 3 is incorrect. - **Option 4 (444):** If $x$ were 444, then substituting back into the equation would give: \[ \frac{444}{1.1} \approx 403.64 \] This does not equal 440, so Option 4 is incorrect. In conclusion, the only value of $x$ that satisfies the equation $\frac{x}{\sqrt{1.21}} = 440$ is 484, making Option 1 the correct choice.

Question

Accepted Answer

To solve the equation $\frac{x}{\sqrt{1.21}} = 440$, we need to find the value of $x$.

1. **Calculate $\sqrt{1.21}$:**

$$
   \sqrt{1.21} = 1.1
   $$

This is because $1.1 \times 1.1 = 1.21$.

2. **Substitute $\sqrt{1.21}$ back into the equation:**

$$
   \frac{x}{1.1} = 440
   $$

3. **Solve for $x$:**

Multiply both sides of the equation by 1.1 to isolate $x$:

$$
   x = 440 \times 1.1
   $$

$$
   x = 484
   $$

Thus, the value of $x$ is 484, which corresponds to Option 1.

**Explanation of why other options are incorrect:**

- **Option 2 (400):** If $x$ were 400, then substituting back into the equation would give:

$$
  \frac{400}{1.1} \approx 363.64
  $$

This does not equal 440, so Option 2 is incorrect.

- **Option 3 (532.4):** If $x$ were 532.4, then substituting back into the equation would give:

$$
  \frac{532.4}{1.1} \approx 484
  $$

While this calculation seems close, it does not match the original equation setup, which requires $x$ to be exactly 484 when multiplied by 1.1 to equal 440. Therefore, Option 3 is incorrect.

- **Option 4 (444):** If $x$ were 444, then substituting back into the equation would give:

$$
  \frac{444}{1.1} \approx 403.64
  $$

This does not equal 440, so Option 4 is incorrect.

In conclusion, the only value of $x$ that satisfies the equation $\frac{x}{\sqrt{1.21}} = 440$ is 484, making Option 1 the correct choice.