Crack DAT General Chemistry Question

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daplton

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I'm having some trouble with concept of molarity, molality, and density.
Question says:
The molarity (X) and molality (Y) of a solution are equal. If the molecular weight of the solute is M, then the density of the solution will be

Answer says:
If the amount of the solute is W g, then it will be W/M mole.
Weight of molal solution = (1000+W)g molality, Y=W/M
If D is the density then its volume will be (1000+W)/D cc
So, molarity, X = W/M * D/(1000+W) * 1000 = Y * 1000/(1000+W) * D
Therefore, D = (1000+W) / 1000 [since x=y]
= 1+ MX/1000 [W = MY = MX]

The part I don't get is how Y = W/M?
amount of solute (in g) / molecular weight of the solute (in g/mole) = mole. If unit is mole how can it be molality (Y)?

Can anybody help?
 
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