Q:

Need help with finding x and y coordinates

"A 1.50 kg particle has the xy coordinates (−1.20 m, 0.500 m) and a 3.50 kg particle has the xy coordinates (0.600 m, −0.750 m). Both lie on a horizontal plane. At what x and y coordinates must you place a 4.00 kg particle such that the center of mass of the three-particle system has the coordinates (−0.500 m, −0.700 m)?
(a) x coordinate
(b) y coordinate "
What I have for x:
(1.5kg) (-1.2 m) + (3.5kg)(0.6m) + (4kg)(x) / 9 kg
How does this simplify?

A:

First, you put parentheses around the three product terms so the whole sum is divided by the $9 kg$.  Second you see that this expression should be equal to $-0.500 m$  Note that $x$ has units of meters.  You have a linear equation to solve for $x$.

