Anonymous
Anonymous asked in Science & MathematicsMathematics · 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.

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  • Anonymous
    1 decade ago
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    1st equation, each area being 1sq foot and defining

    x=area of iridiscent

    y=area of red

    z=area of blue

    1st equation

    x+y+z = 6

    2nd equation

    $45=.75*$6.50*x+.75*$4.50*y+.75*$5.50*z

    4.875x + 3.375y + 4.125z = 45

    3rd equation from there is to be as much iridiscent glass as red and blue glass combined

    x=y+z

    -x+y+z=0

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