let y = the number of 5 dollar cds.
let z = the number of 10 dollar cds.
your first 2 equations are:
x + y + z = 9
2x + 5y + 10z = 60
you are given that the number of 2 and 5 dollar cds that the customer bought was 2 times the number of 10 dollar cds.
your third equation is x + y = 2z
subtract 2z from both sides of this equation to get x + y - 2z = 0
your 3 equations, now set up for matrix operations, are:
x + y + z = 9
2x + 5y + 10z = 60
x + y - 2z = 0
your matrix becomes:
1 1 1 9
2 5 10 60
1 1 -2 0
i used an online gauss jordan calculator to get you the answer.
the answer is:
x = 0
y = 6
z = 3
the gauss jordan calculator that i used can be found at:
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
the results from my use of this calculator are shown below:
while this was done by use of a calculator, the steps involved in arriving at the answer are also shown and you can duplicate them manually if you so desire.
this problem could also have been solved without using the gauss jordan calculator or the matrix method as follows:
your 3 equations that need to be solved simultaneously are:
x + y + z = 9
2x + 5y + 10z = 60
x + y = 2z
in the first equation, replace x + y with 2z to get 2z + z = 9
solve for z to get z = 3
in the first equation, replace z with 3 to get x + y + 3 = 9
solve for x + y to get x + y = 6
solve for x to get x = 6 - y
in the second equation, replace z with 3 and replace x with 6 - y to get:
2x + 5y + 10z = 60 becomes 2 * (6 - y) + 5y + 30 = 60
simplify to get 12 - 2y + 5y + 30 = 60
combine like terms to get 42 + 3y = 60
subtract 42 from both sides to get 3y = 18
solve for y to get y = 6.
since y = 6 and x + y = 6, then x has to be equal to 0.
you get:
x = 0
y = 6
z = 3
this is the same answer that gauss jordan calculator gave you, as it should.
your solutions is:
he 0 two dollar cds and 6 five dollar cds and 3 ten dollar cds.