Let x be the distance between the center of the Earth and the center of gravity of the Earth-Moon system. Taking moments around the center of gravity:

5.98 × 10^{24} (x) = 7.35 × 10^{22} (384.4 × 10^{3} - x)

Solving for x:

5,98 × 10^{24} (x) = 2825.3 × 10^{25} - 7.35 × 10^{22} (x)

598 × 10^{22}(x) + 7.35 × 10^{22}(x) = 2825.3 × 10^{25 }

605.35 × 10^{22}(x) = 2825.3 × 10^{25}

x = (2825.3 x 10^{25})/(605.35 x 10^{22})

x = 4.667 x 10^{3}km