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?
Accepted Solution
A:
Answer:Mason has16 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 has16 20¢ stamps;25 3¢ stamps; 40 49¢ stamps.