Question 6

x = 7.5

To solve for x in the proportion 40:5 = 60:x, we can cross-multiply, leading to the equation 40 * x = 5 * 60. This simplifies to x = (5 * 60) / 40, which equals 7.5.

A) 7.5

Option A is correct because substituting x with 7.5 in the original proportion gives 40:5 = 60:7.5, which holds true since both sides simplify to the same ratio of 8. This confirms that 7.5 is the correct value for x.

B) 1.5

Option B is incorrect because if we set x to 1.5, the proportion becomes 40:5 = 60:1.5. When simplified, the left side equals 8 while the right side equals 40, resulting in an inconsistency.

C) 12

Option C is incorrect as substituting x with 12 in the proportion leads to 40:5 = 60:12. The left side simplifies to 8, while the right side simplifies to 5, indicating that they are not equivalent.

D) 15

Option D is also incorrect because if x is 15, the proportion becomes 40:5 = 60:15. The left side simplifies to 8, whereas the right side simplifies to 4, showing a discrepancy between the two sides.

Conclusion

The correct answer is 7.5, as it accurately satisfies the equation derived from the proportion. All other options fail to provide a valid solution, illustrating that they do not maintain the equality necessary for the original ratio.