Final answer:
After recalculating the ratios with a common denominator and ensuring their sum equals 1 or the whole, the largest amount any sibling could receive from the $169 is $84.48. However, this amount is not an option provided, suggesting a potential issue with the question or answer choices.
Step-by-step explanation:
The question asks how to split a gift of $169 among three siblings in the ratio of 1/2 : 1/3 : 1/4. The first step to solving the problem involves finding a common denominator for these fractions to combine the portions easily. In this case, the common denominator is 12, so the ratios can be converted to 6/12 for 1/2, 4/12 for 1/3, and 3/12 for 1/4. Adding these fractions together gives us 13/12. However, this combined ratio exceeds the intended total of 1 (or 12/12), which suggests a calculation error, as the total of the ratios should be equal to 1.
Correctly recalculating the ratios as parts of the whole (1), they would be 6/12 for 1/2, 4/12 for 1/3, and 3/12 for 1/4, the sum of which is actually 1 (or 12/12). Based on these ratios, the multiplicand for $169 to fit the ratio sum of 12 parts is ($169 / 12 = $14.08). Multiplying the multiplicand by the number of parts each sibling gets: the first sibling receives $14.08 * 6 = $84.48, the second sibling gets $14.08 * 4 = $56.32, and the third sibling receives $14.08 * 3 = $42.24. So the most money any of the siblings could receive is $84.48, which was not one of the provided options indicating a potential error in the question or options given.