Question 7

X = 12.5

To find the value of X in the proportion 4:10 :: 5:X, we can set up the equation 4/10 = 5/X. Cross-multiplying gives us 4X = 50, which simplifies to X = 12.5.

A) X = 10.5

This option is incorrect because substituting X = 10.5 into the proportion results in 4/10 ≠ 5/10.5, which does not hold true. Thus, this value does not satisfy the given ratio.

B) X = 20

This option is also incorrect. If we substitute X = 20 into the proportion, we get 4/10 = 5/20, which simplifies to 4/10 = 1/4. Since these two fractions are not equal, this value does not work for the ratio.

C) X = 12.5

This option is correct because substituting X = 12.5 into the proportion yields 4/10 = 5/12.5. Both ratios simplify to 0.4, confirming that this value maintains the equality of the proportion.

D) X = 25

This option is incorrect as well. When we substitute X = 25, we find 4/10 ≠ 5/25. The left side simplifies to 0.4 while the right side simplifies to 0.2, indicating that this value does not satisfy the proportion.

Conclusion

The correct answer, X = 12.5, maintains the equality of the original ratio. All other options fail to satisfy the proportion due to their inability to maintain the equivalency of the fractions derived from the given ratios. Hence, option C is the only valid solution.