Beginning with an integer $n,$ jake goes through the following steps: $\bullet$ 1. take the reciprocal of the starting number. $\bullet$ 2. double the number obtained in step 1. $\bullet$ 3. take the reciprocal of the number obtained in step 2. at the end of the third step, jake ends up with the number $16.$ what number did jake start with?

n= 32

Jakes started with 32

Step-by-step explanation:

Let n represent the initial integer.

Step 1: take the reciprocal.

Reciprocal of n = 1/n

Step 2: double the number obtained in step 1

= 2×1/n = 2/n

Step 3: take the reciprocal of the number obtained in step 2.

Reciprocal of 2/n = n/2

Since he ended up with 16

n/2 = 16

n = 2×16 = 32

See https://web2.0calc.com/questions/need-help-with-problem_1.

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