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timurjin
4 days ago
9

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?
Mathematics
2 answers:
PIT_PIT [9.1K]4 days ago
6 0
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
babunello [8.4K]4 days ago
3 0

Answer: The cost of the wallet is $60.

Step-by-step explanation: Mr. Wong spent a total of $176 on a jacket, a belt, and a wallet.

The wallet was $31 more expensive than the belt, and the jacket's price was three times that of the belt.

We need to determine the wallet's price.

Let x, y, and z denote the costs of the jacket, belt, and wallet, respectively.

Thus, based on the information given, we derive

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

Substituting the values of z and x from equations (ii) and (iii) into equation (i) yields

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

From equation (ii), we determine

z=31+29=60.

Consequently, the wallet's price is $60.

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