How far from the center of the earth is the center of mass of the earth + moon s

The center of mass of a system consists of a set of obect numbered i=1,2,3... where i has mass ${\displaystyle m_i}$ and is located at position ${\displaystyle (x_i,y_i)}$ is given by:
${\displaystyle x_{cm}=\frac{1}{M}\sum _i{m}_i{x}_i}$ (1)
${\displaystyle y_{cm}=\frac{1}{m}\sum _i{m}_i{y}_i}$ (2)
Given
From the back cover of the book, the mass of earth is ${\displaystyle m_e=5.98\times {10}^{24}kg}$, the mass of Moon is ${\displaystyle m_m=7.36\times {10}^{22}kg}$, and the distnace between them is ${\displaystyle R=3.84\times {10}^8}$ m
Calculations
We can conisder Earth and Moon to be along a straight line, and we ca take this straight line to be the x-axis.
Also we take the origin to be at the center of Earth, so Earths position is ${\displaystyle x_e=0}$ and Moon's position is ${\displaystyle x_m=R}$
Since our system consists of Earrth and Moon only, we can write equation (1) for our system as follows:
${\displaystyle x_{c}m=\frac{m_e{x}_e+m_m{x}_m}{m_e+m_m}}$
Now , we enter the given values, so we get:
${\displaystyle x_{cm}=\frac{0+(7.36\times {10}^{22}kg)(3.84\times {10}^{8}m)}{7.36\times {10}^{22}+5.98\times {10}^{24}kg}=4.67\times {10}^{6}m}$
${\displaystyle x_{cm}=4.67\times {10}^6}$ m
Therefore, the center of mass of the Earth-Moon system is at ${\displaystyle 4.67\times {10}^6}$ m from the center of Earth which is less than Earth's radius ${\displaystyle 6.37\times 1{-}^6}$m