We are given the equation $101_{two} + 12_y = 23_{five}$, and we need to find the value of $y$. The subscripts indicate the base of the number.

1. Problem Description

We are given the equation $101_{two} + 12_y = 23_{five}$, and we need to find the value of $y$. The subscripts indicate the base of the number.

2. Solution Steps

First, we convert each number to base

1

0. $101_{two} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5$.

$12_y = 1 \times y^1 + 2 \times y^0 = y + 2$.

$23_{five} = 2 \times 5^1 + 3 \times 5^0 = 10 + 3 = 13$.

Now we can rewrite the equation in base 10:

$5 + (y + 2) = 13$.

Simplifying the equation, we have

$y + 7 = 13$.

Subtracting 7 from both sides, we get

$y = 13 - 7 = 6$.

3. Final Answer

The value of $y$ is

6. C. 6