Anonymous

# 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.

Relevance

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!!

• Answer to problems with inverse matrices?

Source(s): Aglebra 2