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Mason has a collection of 49¢ stamps, 20¢ stamps, and 34 stamps worth $23.55. He has 56 total 49¢ and 20+ stamps and the number of 3¢ stamps is nine more than the number of 20¢ stamps. How many of each does he have?

Respuesta :

frika

Answer:

Mason has

  • 16 20¢ stamps;
  • 25 3¢ stamps;
  • 40 49¢ stamps.

Step-by-step explanation:

Let x be the number of 20¢ stamps, then the number of 3¢ stamps is  x + 9.

Mason has 56 total 49¢ and 20¢ stamps, then the number of 49¢ stamps is 56 - x.

Amounts:

  • in 49¢: [tex]49(56-x)[/tex] cents;
  • in 20¢: [tex]20x[/tex] cents;
  • in 3¢: [tex]3(x+9)[/tex] cents.

Total amount:

  • [tex]49(56-x)+20x+3(x+9);[/tex]
  • $23.55.

Hence,

[tex]49(56-x)+20x+3(x+9)=2,355\\ \\2,744-49x+20x+3x+27=2,355\\ \\-49x+3x+20x=2,355-2,744-27\\ \\-26x=-416\\ \\26x=416\\ \\x=16[/tex]

Mason has

  • 16 20¢ stamps;
  • 25 3¢ stamps;
  • 40 49¢ stamps.

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