SOLUTION: A stamp collection consists of .06; .13;and .18 stamps. There are 26 stamps in the collection and there are twice as many .13 stamps as there are .06 stamps. The total value of th

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Question 30890: A stamp collection consists of .06; .13;and .18 stamps. There are 26 stamps in the collection and there are twice as many .13 stamps as there are .06 stamps. The total value of the stamps in the collection is $2.92. find the number of .18 stamps in the collection.
Answer by mbarugel(146) (Show Source):
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Hello!
This problem can be solved using a system with 3 unnknowns. Let's call X to the number of 0.06 stamps, Y to the number of 0.13 stanps, and Z to the number of 0.18 stamps.
We have the following data:
"There are 26 stamps in the collection"
The number of stamps is X+Y+Z. So we have:

"there are twice as many .13 stamps as there are .06 stamps"
This means that:

"The total value of the stamps in the collection is $2.92"
The total value of the stamps is given by 0.06X + 0.13Y + 0.18Z. So we have:

We have 3 unknowns and 3 equations. The system we have to solve is:

Let's substitute the 2nd equation into the other two. We're left with:

which is the same as:

Now that we have a 2x2 system of equations, we can solve it using the simple formula:

Solved by pluggable solver: Linear System solver (using determinant)

Solve:

Any system of equations:

has solution

or

(X=8, Z=2}

So we get X = 8 and Z = 2. We also had that Y=2X, so Y = 16. The collection has
8 0.06 stamps
16 0.13 stamps
2 0.18 stamps

I hope this helps!
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