Mason has a collection of .49 stamps, .20 stamps and .3 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

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