Anonymous
Anonymous asked in Education & ReferenceHomework Help · 1 decade ago

Algebra II - Solving Linear Systems (Three Variables) With Inverse Matrices?

I am usually good with word problems, but this one has me stuck.

"You are making mosaic tiles from three types of stained glass. You need 6 squae feet of glass for the project and you want there to be as much iridiscent glass as red and blue glass combined. The cost of a sheet of glass having an area of 0.75 square foot is $6.50 for iridiscent, $4.50 for red, and $5.50 for blue. How many sheets of each type should you purchase if you plan to spend $45 on the project?"

Assume x is for iridiscent, y is for red and z is for blue. What would the three equationgs in the system be? From then on, I can solve it with matrices.

2 Answers

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  • jskud
    Lv 5
    1 decade ago
    Best Answer

    Since there needs to be as much iridiscent and red and blue combined, the first equation is:

    X = Y + Z

    The next thing you know is that all three need to add to 6 square feet:

    X + Y + Z = 6

    We know that the cost for the iridescent can be found by using this equation (ignore the quotes, they are just there for spacing):

    X`````0.75

    __ =____

    ?`````6.50

    so the cost of X is going to be 6.50 X / 0.75

    The cost of Y is going to be 4.50 Y / 0.75

    The cost of Z is going to be 5.50 Z / 0.75

    Finally, we know that the total cost of the final product is $45.

    So,

    (6.50 X / 0.75) + (4.50 Y / 0.75) + (5.50 Z / 0.75) = 45

    We can simplify this by finding a common denominator:

    (6.50 X + 4.50 Y + 5.50 Z) / 0.75 = 45

    Now multiply both sides by 0.75:

    6.50 X + 4.50 Y + 5.50 Z = 33.75

    Hope that helps! Good Luck!!

  • 1 decade ago

    Answer to problems with inverse matrices?

    Source(s): Aglebra 2
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