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3. Si a la suma de un número con 311 se le divide entre 3, a este cociente se le divide entre 36, y a este último cociente se le resta 4, se obtiene 0. ¿Cuál era el número original?

Answer :

To solve the problem of finding the original number, let's go through the steps carefully:

1. Start with the equation given by the problem:
[tex]\[
\left( \left( \frac{x + 311}{3} \right) / 36 \right) - 4 = 0
\][/tex]

2. Isolate the inner terms step-by-step:
- First, add 4 to both sides of the equation:
[tex]\[
\left( \left( \frac{x + 311}{3} \right) / 36 \right) = 4
\][/tex]

3. Eliminate the division by 36:
- Multiply both sides by 36:
[tex]\[
\left( \frac{x + 311}{3} \right) = 4 \times 36
\][/tex]
- Simplify the multiplication:
[tex]\[
\left( \frac{x + 311}{3} \right) = 144
\][/tex]

4. Eliminate the division by 3:
- Multiply both sides by 3:
[tex]\[
x + 311 = 144 \times 3
\][/tex]
- Simplify the multiplication:
[tex]\[
x + 311 = 432
\][/tex]

5. Isolate [tex]\( x \)[/tex]:
- Subtract 311 from both sides:
[tex]\[
x = 432 - 311
\][/tex]
- Simplify the subtraction:
[tex]\[
x = 121
\][/tex]

Therefore, the original number is [tex]\( 121 \)[/tex].

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