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QuestionIn a class of 30 students, 25\frac{2}{5} play sudoku, and 56\frac{5}{6} of those also play checkers. Find how many play both.

Studdy Solution

STEP 1

Assumptions1. The total number of students in Ms. Renault's classroom is30. . 5\frac{}{5} of the students play sudoku.
3. Of the students who play sudoku, 56\frac{5}{6} also play checkers.

STEP 2

First, we need to find the number of students who play sudoku. We can do this by multiplying the total number of students by the fraction of students who play sudoku.
Number of sudoku players=Total number of studentstimesFraction of students who play sudokuNumber\, of\, sudoku\, players = Total\, number\, of\, students \\times Fraction\, of\, students\, who\, play\, sudoku

STEP 3

Now, plug in the given values for the total number of students and the fraction of students who play sudoku to calculate the number of sudoku players.
Number of sudoku players=30times25Number\, of\, sudoku\, players =30 \\times \frac{2}{5}

STEP 4

Calculate the number of students who play sudoku.
Number of sudoku players=30times2=12Number\, of\, sudoku\, players =30 \\times \frac{2}{} =12

STEP 5

Now that we have the number of students who play sudoku, we can find the number of students who play both sudoku and checkers. We can do this by multiplying the number of sudoku players by the fraction of sudoku players who also play checkers.
Number of sudoku and checkers players=Number of sudoku playerstimesFraction of sudoku players who also play checkersNumber\, of\, sudoku\, and\, checkers\, players = Number\, of\, sudoku\, players \\times Fraction\, of\, sudoku\, players\, who\, also\, play\, checkers

STEP 6

Now, plug in the given values for the number of sudoku players and the fraction of sudoku players who also play checkers to calculate the number of students who play both games.
Number of sudoku and checkers players=12times56Number\, of\, sudoku\, and\, checkers\, players =12 \\times \frac{5}{6}

STEP 7

Calculate the number of students who play both sudoku and checkers.
Number of sudoku and checkers players=12times56=10Number\, of\, sudoku\, and\, checkers\, players =12 \\times \frac{5}{6} =10In Ms. Renault's classroom,10 students play both sudoku and checkers.

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