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Mr Tan had some sweets. If he were to give 12 sweets to each student, he would need another 38 sweets. If he were to give 14 sweets to each student, he would need another 58 sweets. How many students did Mr Tan have?

Question

Mr Tan had some sweets. If he were to give 12 sweets to each student, he would need another 38 sweets. If he were to give 14 sweets to each student, he would need another 58 sweets. How many students did Mr Tan have?

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Solution

Let's denote the number of students as 's' and the number of sweets Mr. Tan initially had as 'c'.

From the problem, we have two equations:

  1. c + 38 = 12s
  2. c + 58 = 14s

We can solve this system of equations step by step:

Step 1: Rewrite the first equation to express 'c' in terms of 's': c = 12s - 38

Step 2: Substitute 'c' from the first equation into the second equation: 12s - 38 + 58 = 14s

Step 3: Simplify the equation: 12s + 20 = 14s

Step 4: Solve for 's': 2s = 20, so s = 10

So, Mr. Tan had 10 students.

This problem has been solved

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