Final answer:
To find the number of children, first calculate the value of one ratio unit as 3512 / 8 = 439, given that there are 3512 more men than women. Then, multiply 12 (the ratio units for children) by 439 to get 5268 children. The provided options for the number of children do not include the correct answer, which is 5268.
Step-by-step explanation:
The student's question relates to proportions and solving for an unknown in a given ratio. Given the ratio of men (m) to women (w) to children (c) as 17:9:12, and knowing there are 3512 more men than women, we can set up an equation to find the number of men and then use that to find the number of children. To solve the problem, we use the difference in units between men and women in the ratio (17 - 9 = 8 units) to represent the 3512 men surplus. One unit is therefore equal to 3512 / 8 = 439 men. Now we can calculate the total number of men, women, and children using the ratio units multiplied by this value (17 units for men, 9 units for women, and 12 units for children).
Men = 17 × 439 = 7463
Women = 9 × 439 = 3951 (7463 - 3512)
Since men have 3512 more than women and we already calculated men to be 7463, women would indeed be 7463 - 3512 = 3951.
Children = 12 × 439 = 5268
Therefore, the correct answer for the number of children is 5268, which is not listed as one of the provided options (a, b, c, d).