Question 1

1.2:x::14:42 = 3.6

To solve the proportion 1.2:x::14:42, we can set up the equation 1.2/14 = x/42. Cross-multiplying gives us 1.2 * 42 = 14 * x, leading to x = 3.6.

A) 0.6

Option A is incorrect because substituting 0.6 for x in the proportion 1.2:0.6::14:42 does not satisfy the equality. The ratio 1.2/0.6 simplifies to 2, while 14/42 simplifies to 1/3, which are not equal.

B) 3.6

Option B is correct. Substituting 3.6 for x maintains the proportional relationship: 1.2/14 = 3.6/42 simplifies to 0.0857 on both sides, confirming the equality holds.

C) 1.2

Option C is incorrect because using 1.2 for x gives the ratio 1.2/14, which is not equal to 1.2/42. The two ratios yield different values, demonstrating that they do not maintain the proportion.

D) 2.4

Option D is incorrect as well. If we substitute 2.4 for x, we find that 1.2/14 does not equal 2.4/42. The ratios yield different results, indicating that 2.4 cannot be the correct value for x in this proportion.

Conclusion

The correct answer is 3.6, as it maintains the proportional relationship defined in the question. All other options fail to satisfy the equality established by the original ratios, confirming that 3.6 is the only viable solution.