http://www.forrestrace.com/iridescent-mosaic/
matrices word problem help?
Suppose you are making mosaic tiles from 3 types of stained glass. You need 6 square feet of glass for the project and you want there to be as much iridescent 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 iridescent, $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?
I don’t understand this. Can anyone help?
Thank you.
let x=blue ,y=red and z=iridescent in square feet
then
‘You need 6 square feet of glass’ says
x+y+z=6……………(1)
‘you want there to be as much iridescent glass as red and blue glass combined’ says
x+y=z
that is
x+y-z=0……………..(2)
‘The cost of a sheet of glass having an area of 0.75 square foot is $6.50 for iridescent, $4.50 for red, and $5.50 for blue. How many sheets of each type should you purchase if you plan to spend $45′ says
$4.5/0.75ft^2 =$(4.5/0.75) /ft^2 = $6 /ft^2 for red, and similarly for the others so using this logic
(4.5/0.75)x + (5.5/0.75)y + (6.5/0.75)z = 45
multiplying through by 7.5 gives
45x + 55y + 65z = 337.5…………..(3)
so the matrix can be made from these 3 equations but it is difficult for me to do in matrix notation on yahoo so
subtracting (2) from (1) gives
2z=6 so
z=3
substituting this gives
x+y=3…………………(1*)
45x+55y= 142.5…(2*)
then (2*) – 45*(1*) gives
10y=7.5 so
y=0.75
sub y in (1*) gives
x=3 – 0.75 = 2.25
therefore
x=2.25, y=0.75, z=3 all in ft^2
so
dividing x,y,z by 0.75 gives the number of sheets
red=3, blue=1, iridescent=4
the end
.
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