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There are 4 fewer members in Team Red than Team Blue. If 7 members are transferred from team red to team blue, the total number of numbers in team red becomes 1/3 the numbers of Team blue. How many members are there in Team Red and Team Blue respectively?

Sagot :

YourKaito

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[tex]\mathbb{\huge\red{ANSWER:}}[/tex]

[tex]\sf\large\red{┗━°⌜ 赤い糸 ⌟°━┛}[/tex]

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{INITIAL~ CONDITION}}[/tex]

  • There are 4 fewer members in Team Red than Team Blue.
  • Let the number of members in Team Blue be x.
  • Then, the number of members in Team Red is x - 4.

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{MOVING~MEMBERS}}[/tex]

  • 7 members are transferred from Team Red to Team Blue.
  • This means the number of members in Team Red decreases by 7, and the number of members in Team Blue increases by 7.

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{NEW~MEMBERS~IN~RED}}[/tex]

  • After the transfer, the number of members in Team Red becomes 1/3 the number of members in Team Blue.
  • Let the new number of members in Team Red be y.
  • Then, we have:
  • y = (1/3) x + 7

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{NEW~MEMBERS~IN~BLUE}}[/tex]

  • The number of members in Team Blue increases by 7, so it becomes x + 7.

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{EQUATING~THE~NEW~MEMBERS}}[/tex]

  • Since the new number of members in Team Red is y, we can set it equal to the new number of members in Team Blue, which is x + 7.
  • y = x + 7

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{SUBSTITUTING}}[/tex]

  • (1/3) x + 7 = x + 7.

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{SIMPLIFYING}}[/tex]

  • Subtract 7 from both sides and then subtract x from both sides:
  • (1/3) x = x.

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{MEMBERS~IN~RED}}[/tex]

  • Since the number of members in Team Red is x - 4, we have:
  • x - 4 = 9 - 4 = 5

[tex]\sf{\red{✽}}[/tex] [tex]\bold{\red{MEMBERS~IN~BLUE}}[/tex]

  • The number of members in Team Blue is x + 7, which is:
  • x + 7 = 9 + 7 = 16

[tex]\boxed{\sf\green{✓}}[/tex] Therefore, there are [tex]\bold{\red{5}}[/tex] members in Team Red and [tex]\bold{\blue{16}}[/tex] members in Team Blue.

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