a colection of stamps consist of 2 cent stamps, 8 cent stamps, and 14 cent stamps. The number of 2 cent stamps is five more then twice the number of 8 cent stamps.the number of 14 cent stamps is three times the number of 8 cent stamps. The total value of the stamps is $2.26. Find the number of each type of stamp in the collection.

Question

a colection of stamps consist of 2 cent stamps, 8 cent stamps, and 14 cent stamps. The number of 2 cent stamps is five more then twice the number of 8 cent stamps.the number of 14 cent stamps is three times the number of 8 cent stamps. The total value of the stamps is $2.26. Find the number of each type of stamp in the collection.

Answer 1

Letting x, y, and z equal the numbers of .02, .08 and .14 cent stamps.

1-x = 2y + 5
2-z = 3y
3-.02x + .o8y + .14z = 2.26
4-Times 100 yields 2x + 8y + 14z = 226
5-Substituting (1) and (2) into (4) yields
..2(y + 5) + 8y + 14(3y)
6-Can you take it from here?

Answer 2

Kevin has a total of 92 coin collection .this 8 more than three times the number of quarters in the collections .How many quarters does Kevin have in his collections

Answer 3

To solve this problem, we can set up a system of equations based on the given information.

Let's assume:
x = the number of 2 cent stamps
y = the number of 8 cent stamps
z = the number of 14 cent stamps

Based on the given information, we can create the following equations:

Equation 1: The number of 2 cent stamps is five more than twice the number of 8 cent stamps.
x = 2y + 5

Equation 2: The number of 14 cent stamps is three times the number of 8 cent stamps.
z = 3y

Equation 3: The total value of the stamps is $2.26.
2x + 8y + 14z = 226

Now we have a system of three equations. Let's solve them step-by-step.

Step 1: Substituting Equation 2 and Equation 3 into Equation 1
x = 2y + 5
z = 3y

Substituting z into Equation 1:
x = 2y + 5
14z = 42y

Dividing Equation 2 by 3:
z = 3y

Substituting z into the equation z = 42y:
14(3y) = 42y
42y = 42y

Therefore, we can conclude that Equation 1 is satisfied by the given information.

Step 2: Substituting Equation 1 and Equation 2 into Equation 3

Substituting x into the equation 2x + 8y + 14z = 226:
2(2y + 5) + 8y + 14(3y) = 226
4y + 10 + 8y + 42y = 226
54y + 10 = 226
54y = 216
y = 4

Now we know that the number of 8 cent stamps (y) is 4.

Step 3: Finding the value of x and z

Using Equation 1:
x = 2y + 5
x = 2(4) + 5
x = 8 + 5
x = 13

Using Equation 2:
z = 3y
z = 3(4)
z = 12

So, the number of stamps of each type in the collection is:
2 cent stamps: 13
8 cent stamps: 4
14 cent stamps: 12