To make the ratios even, we multiply each term in the ratio 7:8:9 by 1.5 to obtain the new terms, resulting in the ratio 10.5:12:13.5.
The question asks for a proportional extension of the ratio 7:8:9 into a new ratio where the second term is 12. The general strategy to solve this problem is to find a common multiplier for the terms so that the ratios stay proportional. To keep things even, we calculate the multipliers based on the given numbers. Since 8 is multiplied by 1.5 to get to 12 in the second ratio (8 x 1.5 = 12), we need to multiply the other numbers by the same factor. Multiplying 7 by 1.5, we get 10.5 (as the first term), and multiplying 9 by 1.5, we obtain 13.5 (as the third term). Thus, the complete ratio should be 10.5:12:13.5.