Jjstinidn
Answered

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The ratio of men to women in room A is 5:7 , while the ratio of men to women in room B is 3:2. If there are 105 women in room A and 225 people in room B, what is the ratio of men to women if we combined the two rooms?

Sagot :

Kenjinxidn

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[tex]\rm{\huge{ANSWER:}}[/tex]

ׂ╰┈➤ Ratio of men to women in room A: 5:7

ׂ╰┈➤ Number of women in room A: 105

ׂ╰┈➤ Solving for number of men in room A.

  • [tex]\frac{105}{x}[/tex] = [tex]\frac{7}{5}[/tex]
  • 105 x 5 = 7x
  • 525 = 7x
  • x = 75 men in room A

ׂ╰┈➤ Ratio of men to women in room A: 75:105 = 3:4

ׂ╰┈➤ Ratio of men to women in room B: 3:2

ׂ╰┈➤ Total number of people in room B: 225

ׂ╰┈➤ Solving for number of men in room B.

  • [tex]\frac{(225 ~-~ x)}{x}[/tex] = [tex]\frac{2}{3}[/tex]
  • 225 - x = ([tex]\frac{2}{3}[/tex])x
  • 225 = ([tex]\frac{5}{3}[/tex])x
  • x = 135 men in room B

ׂ╰┈➤ Ratio of men to women in room B: 135:90 = 3:2

ׂ╰┈➤ Total number of men in both rooms: 75 + 135 = 210

ׂ╰┈➤ Total number of women in both rooms: 105 + 90 = 195

ׂ╰┈➤ Ratio of men to women in combined rooms: [tex]\underline{\large\sf\red{210:195}}[/tex] = [tex]\underline{\large\sf\red{14:13}}[/tex]

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