Before:

M   [u][72][20]

A    [u][72]

After:

M   [u][72][20][72]

A    [u]<—-2u—–>

2u = 72+20+72 = 164 = u = 82

Money Mariam had at first = u+72+20 = 82+92 = $174

Substituting 
M – (1/3)M – 96 = 20
(2/3)M = 20 + 96 = 116
M = (3/2)116 = $175 # 

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Thanks sushi88.  I thought I might supplement your answer with one based on equations 🙂

M – A = 20 …(1)

A – 72 =(1/3)(M + 72)
A = (1/3)(M + 72) + 72
A = (1/3)M + 96 …(2)

Substituting (2) into (1):
M – (1/3)M – 96 = 20
(2/3)M = 20 + 96 = 116
M = (3/2)116 = $174 #

This question is slightly poorly worded by “1/3 the amount of money Mariam had” as it makes the reader wonder if it was Mariam’s original sum of money or it is after Mariam had received the money from Azizah.  I think if you do the question by models as you did, you may not see the problem, but the second equation could have been A – 72 = (1/3)M

Hi Chief,

I know it is referring to the after amount for M because I have come across enough Math problems to immediately infer that it is referring to the latest amount.  Also, in Math-English, if they want to make reference to the original amount, they would write it as  “1/3 of the amount Mariam had AT FIRST”.   This is the precise language that typical Math word problem would be written in.

But then again you could be right that they have made a mistake in omitting the “AT FIRST”!!  if the answer differs from the answer key…. lol