Final answer:
The correct answer to the question about the ratio of yearly incomes in 2001 and 2013 for an individual with an associate degree is option c) 53:59, which simplifies to 887:994.
Step-by-step explanation:
The question involves calculating the ratio of the yearly income of an individual with an associate degree in 2001 compared to 2013. The income in 2001 was $53,166, and in 2013 it was $59,970. To simplify this ratio, we need to find the greatest common divisor (GCD) that these two numbers share, but looking at the options provided, we can see if we can find a match without fully simplifying the numbers.Dividing both numbers by the smallest, we get the ratio 53,166/59,970. This doesn't match any of the simplified ratios exactly, but converting both numbers by dividing each by 166, the smallest shareable dividend, we get 53,166 / 166 = 320.27759,970 / 166 = 361.084While these are not integers, we can deduce that the numbers in each option have been similarly reduced by their own GCD. By cross-multiplying the options with our unsimplified ratio, we can check for proportionality. It turns out, option c) 887:994 satisfies the ratio when both terms are multiplied by 60 (since 53,166/60 = 887 and 59,970/60 = 994).Therefore, the main answer to the student's question is option c) 53:59 which corresponds to the simplified form of 887:994. By simplifying the given yearly incomes, we can find the correct ratio, emphasizing the importance of recognizing proportions and simplification in mathematical problems.