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Ala. Ela i Monika maja razem 180 zl. Monika ma 2 razy więcej niz Ala, a Ela 3 razy wieccej niz Monika. Ile pieniędzy ma Monika?

1212. Ala. Ela i Monika maja razem 180180 zl. Monika ma 22 razy więcej niz Ala, a Ela 33 razy wieccej niz Monika. Ile pieniędzy ma Monika?

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Q. 1212. Ala. Ela i Monika maja razem 180180 zl. Monika ma 22 razy więcej niz Ala, a Ela 33 razy wieccej niz Monika. Ile pieniędzy ma Monika?
  1. Define Variables: Let's denote the amount of money that Ala has as AA, Monika has as MM, and Ela has as EE. According to the problem, we have the following relationships:\newline11. A+M+E=180A + M + E = 180 (since they have 180180 zl together)\newline22. M=2AM = 2A (since Monika has twice as much as Ala)\newline33. E=3ME = 3M (since Ela has three times as much as Monika)\newlineWe need to find the value of MM.
  2. Express AA in terms of MM: Using the second relationship, we can express AA in terms of MM: A=M2A = \frac{M}{2}.
  3. Express EE in terms of MM: Using the third relationship, we can express EE in terms of MM: E=3ME = 3M.
  4. Substitute into First Equation: Now we substitute the expressions for AA and EE in terms of MM into the first equation:\newlineM2+M+3M=180\frac{M}{2} + M + 3M = 180.
  5. Combine Like Terms: Combine like terms to solve for MM:4.5M=1804.5M = 180.
  6. Solve for M: Divide both sides of the equation by 4.54.5 to find MM: \newlineM=1804.5.M = \frac{180}{4.5}.
  7. Calculate M: Calculate the value of M:\newlineM=40M = 40.

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