Question
I spent a quarter of my money and then received an amount equal to twice the money I had left. If I now have 30 euros more than at the beginning, how many euros did I have?
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Answer to a math question I spent a quarter of my money and then received an amount equal to twice the money I had left. If I now have 30 euros more than at the beginning, how many euros did I have?
Gerhard
4.590 Answers
Llamemos x euros a la cantidad de dinero con la que empezaste.
Después de gastar un cuarto, te quedan 3x/4 euros.
Luego, recibes el doble del dinero que te quedaba, que es 2*(3x/4) = 3x/2 euros.
La cantidad total que tienes ahora es 3x/4 (dinero restante) + 3x/2 (dinero recibido) = 9x/4 euros.
Como son 30 euros más de lo que empezaste, podemos escribir la ecuación:
9x/4 = x + 30
Resolviendo para x:
Multiplica ambos lados por 4 para deshacerte de la fracción:
9x = 4x + 120
Resta 4x de ambos lados para aislar x:
5x = 120
Divide ambos lados por 5 para encontrar x:
x = 24
Por lo tanto, originalmente tenías 24 €.
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