Question

Mr Wong spent a total of $176 on a jacket a belt and a wallet. The wallet cost $31 more than a belt. The jacket cost 3 times as much as the belt. How much did the wallet cost?

Answer 1

Wallet = belt + 31
jacket = 3 · belt

176 = belt + wallet + jacket

176 = belt + (belt + 31) + (3 · belt)
176 = (2 · belt) + 31 + (3 · belt)
176 = (5 · belt) + 31
5 ·belt = 145
belt = 29

Answer 2

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

$x+y+z=176~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\z=y+37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\x=3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the values of z and x from equations (ii) and (iii) in equation (i), we get

$3y+y+y+31=176\\\\\Rightarrow 5y=176-31\\\\\Rightarrow 5y=145\\\\\Rightarrow y=\dfrac{145}{5}\\\\\Rightarrow y=29.$

From equation (ii), we get

$z=31+29=60.$

Thus, the required cost of the wallet is $60.