x varies inversely as y. When x=3.5, then y=2.4. What is the value of y when x=5.6 ?

Q: x varies inversely as y. When x=3.5, then y=2.4. What is the value of y when x=5.6 ?

To solve the problem where $ x $ varies inversely as $ y $, we use the relationship $ x \times y = k $, where $ k $ is a constant. Given that when $ x = 3.5 $, $ y = 2.4 $, we can find the constant $ k $ as follows: \[ k = x \times y = 3.5 \times 2.4 = 8.4 \] Now, we need to find the value of $ y $ when $ x = 5.6 $. Using the inverse variation relationship: \[ x \times y = k \] Substitute the known values: \[ 5.6 \times y = 8.4 \] To find $ y $, divide both sides by 5.6: \[ y = \frac{8.4}{5.6} = 1.5 \] Thus, the value of $ y $ when $ x = 5.6 $ is 1.5, which corresponds to Option 2. **Explanation of why each option is incorrect except Option 2:** 1. **Option 1 (1.4):** If $ y $ were 1.4, then $ 5.6 \times 1.4 = 7.84 $, which does not equal the constant $ k = 8.4 $. Therefore, this option is incorrect. 2. **Option 3 (2.1):** If $ y $ were 2.1, then $ 5.6 \times 2.1 = 11.76 $, which is also not equal to the constant $ k = 8.4 $. Thus, this option is incorrect. 3. **Option 4 (2.8):** If $ y $ were 2.8, then $ 5.6 \times 2.8 = 15.68 $, which again does not equal the constant $ k = 8.4 $. Hence, this option is incorrect. Therefore, the only correct answer, as supported by the calculations and reasoning, is Option 2 (1.5).

Question

Accepted Answer

To solve the problem where $ x $ varies inversely as $ y $, we use the relationship $ x \times y = k $, where $ k $ is a constant. Given that when $ x = 3.5 $, $ y = 2.4 $, we can find the constant $ k $ as follows:

$$ k = x \times y = 3.5 \times 2.4 = 8.4 $$

Now, we need to find the value of $ y $ when $ x = 5.6 $. Using the inverse variation relationship:

$$ x \times y = k $$

Substitute the known values:

$$ 5.6 \times y = 8.4 $$

To find $ y $, divide both sides by 5.6:

$$ y = \frac{8.4}{5.6} = 1.5 $$

Thus, the value of $ y $ when $ x = 5.6 $ is 1.5, which corresponds to Option 2.

**Explanation of why each option is incorrect except Option 2:**

1. **Option 1 (1.4):** If $ y $ were 1.4, then $ 5.6 \times 1.4 = 7.84 $, which does not equal the constant $ k = 8.4 $. Therefore, this option is incorrect.

2. **Option 3 (2.1):** If $ y $ were 2.1, then $ 5.6 \times 2.1 = 11.76 $, which is also not equal to the constant $ k = 8.4 $. Thus, this option is incorrect.

3. **Option 4 (2.8):** If $ y $ were 2.8, then $ 5.6 \times 2.8 = 15.68 $, which again does not equal the constant $ k = 8.4 $. Hence, this option is incorrect.

Therefore, the only correct answer, as supported by the calculations and reasoning, is Option 2 (1.5).