Final answer:
To maintain the ratio of 11:12, after j is multiplied by 17, k must be multiplied by 17/11. The calculation involves setting up a proportion and solving for the multiplier.
Step-by-step explanation:
To maintain the same ratio after multiplying j by 17, k must be multiplied by 17/11. This ensures that the ratio of j to k, which is 11:12, remains constant even after the multiplication. To maintain the same ratio between j and k, if j is multiplied by 17, k should be multiplied by the same factor. The original ratio is 11:12, so if j is multiplied by 17, the new ratio would be 187:12. Therefore, k should be multiplied by 187 in order to maintain the same ratio.
Initially, we have j/k = 11/12. Multiplying j by 17, we get 17j. We need to find a number x such that when we multiply k by x, the new ratio is the same, so (17j)/(kx) = 11/12. By cross-multiplying, 17j * 12 = 11kx. Since j/k = 11/12, we can replace j with 11/12k, yielding (17 * 11/12k) * 12 = 11kx. Simplifying this, we get 17k = kx, which means x = 17. This is the value we need to multiply k by to maintain the ratio, hence x = 17/11.