What Is the Distance from the Center of the Moon $5.97 \times 10 ^ { 24 } \mathrm {~kg}$

Multiple Choice

What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the mass of the Moon is $7.35 \times 10 ^ { 22 } \mathrm {~kg}$ the center-to-center distance between Earth and the Moon is 3.84 \times $10 ^ { 8 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$

A) $3.84 \times 10 ^ { 7 } \mathrm {~m}$
B) $3.83 \times 10 ^ { 6 } \mathrm {~m}$
C) $4.69 \times 10 ^ { 7 } \mathrm {~m}$
D) $4.69 \times 10 ^ { 6 } \mathrm {~m}$
E) $3.45 \times 10 ^ { 8 } \mathrm {~m}$