Answer: The required cost of the wallet is $60.
Step-by-step explanation: Given that Mr Wong spent a total of $176 on a jacket a belt and a wallet.
The wallet cost $31 more than a belt and the jacket cost 3 times as much as the belt.
We are to find the cost of the wallet.
Let x, y and z represents the cost of the jacket, the belt and the wallet respectively.
Then, according to the given information, we have
[tex]x+y+z=176~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\z=y+37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\x=3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the values of z and x from equations (ii) and (iii) in equation (i), we get
[tex]3y+y+y+31=176\\\\\Rightarrow 5y=176-31\\\\\Rightarrow 5y=145\\\\\Rightarrow y=\dfrac{145}{5}\\\\\Rightarrow y=29.[/tex]
From equation (ii), we get
[tex]z=31+29=60.[/tex]
Thus, the required cost of the wallet is $60.
