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At a baseball game, there were three times as many males as females, 5/6 of the males were boys and the rest were men, 2/3 of the females were girls and the rest were women. Given that there were 121 more boys than the girls, how many adults were there at the baseball game?

Respuesta :

frika

Answer:

55

Step-by-step explanation:

Let x  be the number of females at a baseball game. There were three times as many males as females, then the number of males is 3x.

5/6 of the males were boys and the rest were men, then

  • [tex]\dfrac{5}{6}\cdot 3x=\dfrac{5x}{2}[/tex] is the number of boys;
  • [tex]\left(1-\dfrac{5}{6}\right)\cdot 3x=\dfrac{1}{6}\cdot 3x=\dfrac{x}{2}[/tex] is the number of men.

2/3 of the females were girls and the rest were women, then

  • [tex]\dfrac{2}{3}x[/tex] is the number of girls;
  • [tex]\left(1-\dfrac{2}{3}\right)\cdot x=\dfrac{1}{3}x[/tex] is the number of women.

There were 121 more boys than the girls, thus

[tex]\dfrac{5x}{2}-\dfrac{2x}{3}=121\\ \\\dfrac{5x\cdot 3-2x\cdot 2}{6}=121\\ \\15x-4x=121\cdot 6\\ \\11x=726\\ \\x=66[/tex]

There were 66 females and 198 males.

The number of men [tex]=\dfrac{66}{2}=33;[/tex]

The number of women [tex]=\dfrac{66}{3}=22;[/tex]

The total number of adults[tex]=33+22=55.[/tex]

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