SOLUTION: Hi there, appreciate your help please on solving this hard word problem below
Mr Jone works in a music shop in Nabua. Over the last three weeks there has been a sale, and music
Question 1115404: Hi there, appreciate your help please on solving this hard word problem below
Mr Jone works in a music shop in Nabua. Over the last three weeks there has been a sale, and music CDs in the Jumbo bin have been sold for $2, $5 or $10. One of Mr Jone’s customers bought a total of nine CDs. The total cost for buying the nine CDs was $60. The combined number of $2 and $5 CDs that the customer bought was twice as many as the number of $10 CDs that he bought.
i. Set up the system of equations.
ii. Using Gauss Jordan Elimination Method, solve this system of equations to find the number of $10, $20, and $25 CDs that the customer bought.
Thank you
You can put this solution on YOUR website! let x = the number of 2 dollar cds.
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:
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:
