Question

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?

Answer 1

Answer: n= 32

Jakes started with 32

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