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Aloysius had some money at first. He spent $360 on a suit. He then spent 1/7 of his remaining money on shoes and had 2/5 of his money left. How much money did he have at first?

 May 6, 2024
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For this problem, you would have to set the amount of money as a variable. 

 

They key is to essentially write a solvable equation to figure it out!

 

In fact, my parents used to give me a lot of problems similar to this one :)

 

So let's let that be x. 

 

From the problem, we can get the equation \(\frac{2}{5}x+\frac{1}{7}(x-360)+360=x\)

 

We have \(\frac{2}{5}x + \frac{1}{7}x - \frac{360}{7}+360 = x\). Combining like terms and isolating x, we have \(\frac{2160}{7}=\frac{16}{35}x\)

 

We multiply both sides by 35/16, and we have \(\frac{35}{16} \cdot \frac{2160}{7} = x\)

 

So we have \(x = 675\)

 

$675!

 

Thanks!

 May 6, 2024

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