Answer: Mason has 40 forty-nine cent stamps, 16 twenty cent stamps and 25 three cent stamps
Step-by-step explanation:
Let x represent the number of 49 cent stamps that Mason has.
Let y represent the number of 20 cent stamps that Mason has.
Let z represent the number of 3 cent stamps that Mason has.
Mason has a collection of 49 cent stamps, 20 cent stamps, and 3 cent stamps worth $23.55. This means that
0.49x + 0.2y + 0.03z = 23.55 - - - - -1
He had 56 total 49 cent and 20 cent stamps. This means that
x + y = 56
x = 56 - y
The number of 3 cent stamps is nine more than the number of 20 cent stamps. This means that
z = y + 9
Substituting x = 56 - y and z = y + 9 into equation 1, it becomes
0.49(56 - y) + 0.2y + 0.03(y + 9) = 23.55
27.44 - 0.49y + 0.2y + 0.03y + 0.27 = 23.55
27.44 + 0.27 - 0.49y + 0.2y + 0.03y = 23.44
27.71 - 0.26y = 23.55
- 0.26y = 23.55 - 27.71
- 0.26y = - 4.16
y = - 4.16/ - 0.26y
y = 16
x = 56 - y = 56 - 16
x = 40
z = y + 9 = 16 + 9
z = 25
