This problem involves ratios and a bit of algebra. Here's how to solve it:

Step 1: Let's denote the scores of A, B, C, D, and E as a, b, c, d, and e respectively. From the problem, we know that a/d = 8/12 and d/e = 12/13. We also know that b/e = 11/7 and c/e = 9/7.

Step 2: From the ratios, we can express a, b, c, and d in terms of e. We get a = 8d/12 = 2d/3, b = 11e/7, c = 9e/7, and d = 12e/13.

Step 3: We know that either b or c scored 117 marks. So, we can set b = 117 or c = 117 and solve for e. If b = 117, we get e = 7*117/11 = 77. If c = 117, we get e = 7*117/9 = 91.

Step 4: We also know that the maximum score is 200. So, we need to check if e = 77 or e = 91 gives a, b, c, d, and e all less than or equal to 200. If e = 77, we get a = 2*12*77/39 = 72, b = 117, c = 9*77/7 = 99, and d = 12*77/13 = 72. If e = 91, we get a = 2*12*91/39 = 84, b = 11*91/7 = 143, c = 117, and d = 12*91/13 = 84.

Step 5: The difference between the highest and the lowest scores is the answer to the problem. If e = 77, the difference is 117 - 72 = 45. If e = 91, the difference is 143 - 84 = 59. So, the answer is 59.

Question

This problem involves ratios and a bit of algebra. Here's how to solve it:

Step 1: Let's denote the scores of A, B, C, D, and E as a, b, c, d, and e respectively. From the problem, we know that a/d = 8/12 and d/e = 12/13. We also know that b/e = 11/7 and c/e = 9/7.

Step 2: From the ratios, we can express a, b, c, and d in terms of e. We get a = 8d/12 = 2d/3, b = 11e/7, c = 9e/7, and d = 12e/13.

Step 3: We know that either b or c scored 117 marks. So, we can set b = 117 or c = 117 and solve for e. If b = 117, we get e = 7*117/11 = 77. If c = 117, we get e = 7*117/9 = 91.

Step 4: We also know that the maximum score is 200. So, we need to check if e = 77 or e = 91 gives a, b, c, d, and e all less than or equal to 200. If e = 77, we get a = 2*12*77/39 = 72, b = 117, c = 9*77/7 = 99, and d = 12*77/13 = 72. If e = 91, we get a = 2*12*91/39 = 84, b = 11*91/7 = 143, c = 117, and d = 12*91/13 = 84.

Step 5: The difference between the highest and the lowest scores is the answer to the problem. If e = 77, the difference is 117 - 72 = 45. If e = 91, the difference is 143 - 84 = 59. So, the answer is 59.

Knowee AI · Accepted Answer

This problem involves ratios and a bit of algebra. Here's how to solve it:

Step 1: Let's denote the scores of A, B, C, D, and E as a, b, c, d, and e respectively. From the problem, we know that a/d = 8/12 and d/e = 12/13. We also know that b/e = 11/7 and c/e = 9/7.

Step 2: From the ratios, we can express a, b, c, and d in terms of e. We get a = 8d/12 = 2d/3, b = 11e/7, c = 9e/7, and d = 12e/13.

Step 3: We know that either b or c scored 117 marks. So, we can set b = 117 or c = 117 and solve for e. If b = 117, we get e = 7*117/11 = 77. If c = 117, we get e = 7*117/9 = 91.

Step 4: We also know that the maximum score is 200. So, we need to check if e = 77 or e = 91 gives a, b, c, d, and e all less than or equal to 200. If e = 77, we get a = 2*12*77/39 = 72, b = 117, c = 9*77/7 = 99, and d = 12*77/13 = 72. If e = 91, we get a = 2*12*91/39 = 84, b = 11*91/7 = 143, c = 117, and d = 12*91/13 = 84.

Step 5: The difference between the highest and the lowest scores is the answer to the problem. If e = 77, the difference is 117 - 72 = 45. If e = 91, the difference is 143 - 84 = 59. So, the answer is 59.

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