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How many total questions are in a 4-hour exam if there are 60 mathematics problems and each one requires twice the time allocated for the other questions?

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To determine the total number of questions in a 4-hour exam, knowing that there are 60 mathematics problems which require twice the time allocated for each of the other questions, we can approach the problem methodically.

First, let's convert the total time into minutes: 4 hours equates to 240 minutes.

Next, since the mathematics problems require twice the time of the other questions, we can denote the time taken for one mathematics problem as 2t, and the time taken for each of the other questions as t.

If there are a total of N questions on the exam, this would include the 60 mathematics problems and (N - 60) other questions. The total time spent on the exam can then be expressed as:

- Time for mathematics problems: 60 problems × 2t = 120t

- Time for other questions: (N - 60) problems × t = (N - 60)t

Now, we can create an equation representing the total time used for the exam:

120t + (N - 60)t = 240.

Combining the like terms gives:

(120 + N - 60)t = 240

(60 + N)t = 240.

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