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At the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults at the movie.
How many children are at the movie?
children

At the newest animated movie, for every 99 children, there are 44 adults. There are a total of 3939 children and adults at the movie.\newlineHow many children are at the movie?\newlinechildren

Full solution

Q. At the newest animated movie, for every 99 children, there are 44 adults. There are a total of 3939 children and adults at the movie.\newlineHow many children are at the movie?\newlinechildren
  1. Ratio Relationship: Let's denote the number of children as CC and the number of adults as AA. According to the problem, for every 99 children, there are 44 adults. This gives us the ratio of children to adults as 9:49:4. We can express this relationship as CA=94\frac{C}{A} = \frac{9}{4}.
  2. Total Number Equation: We also know that the total number of children and adults is 3939. This gives us the equation C+A=39C + A = 39.
  3. Express AA in terms of CC: To find the number of children, we need to solve the system of equations:\newline11) CA=94\frac{C}{A} = \frac{9}{4}\newline22) C+A=39C + A = 39\newlineWe can express AA in terms of CC using the first equation: A=(49)CA = \left(\frac{4}{9}\right)C.
  4. Substitute AA into Equation: Substitute A=49CA = \frac{4}{9}C into the second equation: C+49C=39C + \frac{4}{9}C = 39.
  5. Combine Like Terms: Combine like terms: 1+491 + \frac{4}{9}C = 3939. This simplifies to 99+49\frac{9}{9} + \frac{4}{9}C = 3939, which is 139\frac{13}{9}C = 3939.
  6. Solve for C: To find C, we multiply both sides of the equation by the reciprocal of (139)(\frac{13}{9}), which is (913)(\frac{9}{13}): C=39×(913)C = 39 \times (\frac{9}{13}).
  7. Calculate Number of Children: Calculate CC: C=39×(913)=3×9=27C = 39 \times \left(\frac{9}{13}\right) = 3 \times 9 = 27. So there are 2727 children at the movie.