Annie is building a diorama for her history class. The amount of time she spent building it is equal to three times the amount of time she spent planning it minus 5 minutes. If she spent 67 minutes on the diorama total, how many minutes did she spend building it?
Stream of thoughts:
49
Let p be the planning time in minutes and b be the building time.

We know that b = 3p - 5 and b + p = 67.

Substituting the first equation into the second equation, we get 3p - 5 + p = 67.

Combining like terms, we get 4p - 5 = 67.

Adding 5 to both sides, we get 4p = 72.

Dividing both sides by 4, we get p = 18.

Substituting this value into b = 3p - 5, we find that b = 3 * 18 - 5 = 49.

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Thus, the answer is 49