Question

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?

Answer 1

Mason has

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

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¢:
  `49(56-x)` cents;
• in 20¢:
  `20x` cents;
• in 3¢:
  `3(x+9)` cents.

Total amount:

• 
  `49(56-x)+20x+3(x+9);`
• $23.55.

Hence,

`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`

Mason has

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