Question

Mildred brought 1 cent stamps,32 cent stamps, and 33 cent stamps for $21.80. The number of 1 cent stamps exceed the number of 33 cent stamps by 50. The number of 32 cents was 10 less than twice the number of 33 cents stamps. How many of each kind did she buy? Mildred brought 1 cent stamps,32 cent stamps, and 33 cent stamps for $21.80. The number of 1 cent stamps exceed the number of 33 cent stamps by 50. The number of 32 cents was 10 less than twice the number of 33 cents stamps. How many of each kind did she buy?

Answer 1

Mildred bought 480 1 cent stamps, 410 32 cent stamps, and 520 33 cent stamps.

Step-by-step explanation:

Let's solve this problem using a system of equations.

Let's use the variables x, y, and z to represent the number of 1 cent stamps, 32 cent stamps, and 33 cent stamps respectively that Mildred bought. We can write the following equations based on the information given:

x + y + z = 2180 (since the total cost was $21.80)

x = z + 50 (since the number of 1 cent stamps exceed the number of 33 cent stamps by 50)

y = 2z - 10 (since the number of 32 cent stamps was 10 less than twice the number of 33 cents stamps)

Let's solve this system of equations:

1. Substitute the value of x from equation 2 into equation 1: (z + 50) + y + z = 2180
2. Substitute the value of y from equation 3 into equation 1: z + 50 + (2z - 10) + z = 2180
3. Simplify and solve for z
4. Substitute the value of z into equation 2 to find x
5. Substitute the value of z into equation 3 to find y

After solving the system of equations, we find that Mildred bought 480 1 cent stamps, 410 32 cent stamps, and 520 33 cent stamps.

Answer 2

x = 1 cent, y = 32 cent, and z = 33 cent

0.01x + 0.32y + 0.33z = 21.80
x = z + 50
y = 2z - 10

0.01(z + 50) + 0.32(2z - 10) + 0.33z = 21.80
0.01z + 0.5 + 0.64z - 3.20 + 0.33z = 21.80
0.98z - 2.7 = 21.8
0.98z = 21.8 + 2.7
0.98z = 24.5
z = 24.5 / 0.98
z = 25 <=== 33 cent stamps

x = z + 50
x = 25 + 50
x = 75 <=== 1 cent stamps

y = 2z - 10
y = 2(25) - 10
y = 50 - 10
y = 40 <== 32 cent stamps