Final answer:
The value of k is 12 (option A)
Step-by-step explanation:
To find the value of k in the proportion 10/6 = 21/k, we can cross-multiply and solve for k.
- Multiply 10 by k: 10 * k = 10k.
- Multiply 6 by 21: 6 * 21 = 126.
- Set the two products equal to each other: 10k = 126.
- Divide both sides by 10 to solve for k: k = 126 / 10 = 12.6.
However, we are only given the options A) 12, B) 14, C) 18, D) 24. Since 12.6 is not an option, and the closest value is 12, we could suspect a typo in the original problem or in the available options. If it was indeed a typo and the original proportion is supposed to have integer solutions, the most reasonable choice given the context is A) 12.