Ethan and Noah saved the same amount of money. Noah spent $162 buying a birthday gift for her friend. In the end, Ethan had 4 times as much as Noah. How much did Ethan have?
Question
Ethan and Noah saved the same amount of money. Noah spent $162 buying a birthday gift for her friend. In the end, Ethan had 4 times as much as Noah. How much did Ethan have?
Solution
Let's solve this step by step:
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Let's denote the amount of money that Ethan and Noah saved as X.
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After buying a birthday gift, Noah has X - $162 left.
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According to the problem, Ethan has 4 times as much as Noah has left, so Ethan has 4 * (X - $162).
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But Ethan didn't spend any money, so he still has X.
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Therefore, we can set up the equation X = 4 * (X - $162).
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If we simplify this equation, we get X = 4X - 648.
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If we move 4X to the left side of the equation, we get -3X = -648.
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If we divide both sides of the equation by -3, we get X = 216.
So, Ethan has $216.
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