Mr. Dinkelspiel bought $32.56 worth of stamps. He bought 20 more 19-cent stamps than 50-cent stamps. He bought twice as many 32-cent stamps as 19- cent stamps. How many of each kind did he buy?

He bought x 50-cent stamps.

He bought x+20 19-cent stamps.
He bought 2(x+20) 32-cent stamps.

50*x + 19(x+20) + 32*2(x+20)=3256
x=12

x+20 = 12+20=32 19-cent stamps.

2(x+20)=2*32=64

So he bought 12 50-cent stamps, 32 19-cent stamps and 64 32-cent stamps.

Let's solve this step by step.

Let's assume that Mr. Dinkelspiel bought x 50-cent stamps.

According to the problem, he bought 20 more 19-cent stamps than 50-cent stamps. So, the number of 19-cent stamps will be (x + 20).

He also bought twice as many 32-cent stamps as 19-cent stamps. So, the number of 32-cent stamps will be 2(x + 20).

Now, let's calculate the total cost of the stamps:

The cost of 50-cent stamps = 50 * x
The cost of 19-cent stamps = 19 * (x + 20)
The cost of 32-cent stamps = 32 * 2(x + 20)

According to the problem, the total cost of all the stamps is $32.56. So, we can equate the total cost to $32.56:

50x + 19(x + 20) + 32 * 2(x + 20) = 32.56

Now, let's solve this equation to find the value of x.

50x + 19x + 380 + 64(x + 20) = 32.56
50x + 19x + 380 + 64x + 1280 = 32.56
133x + 1660 = 32.56
133x = 32.56 - 1660
133x = -1627.44
x = -1627.44 / 133
x = -12.2306

Since we can't have negative stamps, it appears that there is an error in the problem or the data provided.

Please check the problem statement or the data given.

To solve this problem, we can use a system of equations. Let's assign variables to the unknown values.

Let's say:
x = the number of 50-cent stamps
y = the number of 19-cent stamps
z = the number of 32-cent stamps

From the given information, we can write three equations:

1. The total value of the stamps is $32.56:
0.50x + 0.19y + 0.32z = 32.56

2. Mr. Dinkelspiel bought 20 more 19-cent stamps than 50-cent stamps:
y = x + 20

3. He bought twice as many 32-cent stamps as 19-cent stamps:
z = 2y

To solve the system, we can substitute equations 2 and 3 into equation 1. Let's do that.

0.50x + 0.19(x + 20) + 0.32(2x + 40) = 32.56

Now, simplify and solve the equation:

0.50x + 0.19x + 3.80 + 0.64x + 12.80 = 32.56
1.33x + 16.60 = 32.56
1.33x = 32.56 - 16.60
1.33x = 15.96
x = 15.96 / 1.33
x ≈ 12

We found the value for x, which means he bought 12 50-cent stamps.

Now, we can substitute this back into equation 2 to find the number of 19-cent stamps:

y = x + 20
y ≈ 12 + 20
y ≈ 32

So, he bought approximately 32 19-cent stamps.

Lastly, using equation 3, we can find the number of 32-cent stamps:

z = 2y
z = 2 * 32
z = 64

Therefore, Mr. Dinkelspiel bought 12 50-cent stamps, 32 19-cent stamps, and 64 32-cent stamps.