Final answer:
To maintain the ratio of j to k (11:12) when j is multiplied by 17, k must also be multiplied by 17.
Step-by-step explanation:
The question asks us to find the factor by which k should be multiplied to maintain the ratio of j to k (which is 11:12) when j is multiplied by 17. First, we need to represent the given ratio algebraically, which can be expressed as j:k = 11:12. If we multiply j by 17, to keep the ratio same, the equation becomes 17j: k' = 11:12, where k' is the new value of k.
To find out what k should be multiplied by, we need to set up a proportion. Therefore, 17j/j = k'/k. Simplifying this, we get 17 = k'/k. Answering the question, k should be multiplied by 17 to maintain the same ratio after j has been multiplied by 17.
To maintain the same ratio between j and k when j is multiplied by 17, we need to find the value of k. In the given ratio, j:k is 11:12. After multiplying j by 17, the new ratio becomes 17j:k. Since we want the ratio to remain the same, we need to find the value of k that maintains the ratio 17j:k as 11:12.
To do this, we can set up a proportion: (17j) / k = 11 / 12. Cross multiplying and solving for k, we get k = (12 * 17j) / 11.
So, k should be multiplied by (12 * 17) / 11 to maintain the same ratio when j is multiplied by 17.