Glass Mosaic Kitchen
Algebra 2 problem, need help please!?
You need 9 square feet of Glass Mosaic Tiles to decorate a wall of your kitchen. You want the area of the red tiles to equal the combned area of the yellow and blue tiles. The cost of a sheet of glass tiles having an area of .75 square foot is $6.50 for red, $4.50 for yellow, and $8.50 for blue. You have $80 to spend.
a) write a system of equations to represent this situation.
b) write the system as a matrix equation.
If you could help with A or B that would be so helpful!
y will represent # of yellow tiles, b, the number of blue tiles, and r the number of red tiles
First, use the first information given, "you need 9 sq. feet of tiles" and "tiles have an area of .75 ft sq.
9=.75y+.75b+.75r
(the total area = area of one tile times the number of yellow tiles + the number of blue tiles + the number of red tiles)
Then use the ratio of tiles that is given - "the area of the red tiles equals the combined area of the blue tiles
.75r=.75b+.75b
(the area of one tile times the number of red tiles = the area of one tile times the number of blue tiles + the number of yellow tiles)
Finally, the pricing
80=6.5r+4.5y+8.5b
(the total amount you have to spend = the pricing of one red tile times the number of red tiles + the pricing of one yellow tile times the number of yellow tiles + the pricing of one blue tile times the number of blue tiles
that is your system, with this, putting it into a matrix will be easy.
Make sure you know why all of this is so, otherwise, it will be pointless.
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