Question

Three masses of 4.0 kg, 5.0 kg and 7.0 kg are located on a line at positions +4.0, +8.0, and -5.0 in meters from the origin, respectively. Where is the center of mass of these three masses?

With respect to the origin as x = 0, I calculated the center of mass to be:
(4.0 kg)*(4.0 m)+(5.0 kg)*(8.0 m)+(7.0 kg)*(-5.0 m), all divided by the total mass of 16 kg. This gives an answer of 1.3125 m to the positive side of the origin.

However the answer in the book says the centre of mass is located at 1.0 m. I don't know where I went wrong.

Answer 1

(4 * 4) + (8 * 5) > 7 * 5
... so the CM is > 0

[4*(4-x)]+[5*(8-x)]-[7*(5+x)] = 0