Questions: Una persona tiene 100000 en 30 billetes, algunos de 2000 y el resto de 10000. ¿Cuántos billetes más tiene de 2000 que de 10000?

Una persona tiene 100000 en 30 billetes, algunos de 2000 y el resto de 10000. ¿Cuántos billetes más tiene de 2000 que de 10000?
Transcript text: Una persona tiene $\$ 100000$ en 30 billetes, algunos de $\$ 2000$ y el resto de $\$ 10000$. ¿Cuántos billetes más tiene de $\$ 2000$ que de $\$ 10000$ ?
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Solution

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To solve this problem, we need to determine the number of \$2000 bills and \$10000 bills that make up a total of 30 bills and \$100000. We can set up a system of equations: let \( x \) be the number of \$2000 bills and \( y \) be the number of \$10000 bills. The equations are: \( x + y = 30 \) and \( 2000x + 10000y = 100000 \). Solving this system will give us the values of \( x \) and \( y \), and we can then find how many more \$2000 bills there are than \$10000 bills.

Paso 1: Definición de variables

Sea \( x \) el número de billetes de \$2000 y \( y \) el número de billetes de \$10000. Según el problema, tenemos las siguientes ecuaciones:

  1. \( x + y = 30 \)
  2. \( 2000x + 10000y = 100000 \)
Paso 2: Resolución del sistema de ecuaciones

Resolviendo el sistema de ecuaciones, encontramos que:

  • \( x = 25 \)
  • \( y = 5 \)
Paso 3: Cálculo de la diferencia

Para encontrar cuántos billetes más tiene de \$2000 que de \$10000, calculamos la diferencia:

\[ x - y = 25 - 5 = 20 \]

Respuesta Final

La respuesta es \( \boxed{20} \).

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