Daniel has a collection of stamps worth $6. He has 5 more 8 cent stamps then 30 cent stamps. The number of 6 cent stamps is 2 times the amount of 30 cent stamps. The number of 5 cent stamps is 12. How many of each kind of stamps does Daniel have? Please list the number of 30, 5, 6, 8 cent stamps he has.
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12 of the 5 cents stamps,

20 of the 6 cents stamps

15 of the 8 cents stamps

10 of the 30 cents stamps.

Step-by-step explanation:

Let's name:

x = number of 5 cent stamps,

w = number of 6 cent stamps,

y = number of 8 cent stamps,

z = number of 30 cent stamps,

Create the following system of equations based on the info provided:

z + 5 = y

w = 2 * z

x = 12

600 = 5 (12) + 6 w + 8 y + 30 z

replace everything in terms of "z":

600 = 60 + 6 (2 * z) + 8 (z + 5) + 30 z

540 = 12 z + 8 z + 40 + 30 z

500 = 50 z

z = 10

and now we can find the rest:

y = 5 + 10 = 15

w = 2 * 10 = 20

Therefore there are:

12 of the 5 cents stamps,

20 of the 6 cents stamps

15 of the 8 cents stamps

10 of the 30 cents stamps.

529 and 531

step-by-step explanation: