If there are e erasers, p pencils, and q pens, we have
2e+4p = 240
6e+p+2q = 395
e+p+4q = 415
If A is the matrix of coefficients, then A^-1 =
1/84
(-2 16 -8)
(22 -8 4)
(-5 -2 22)
Then you have
(e p q) = (30 45 85)
See here:
http://www.wolframalpha.com/input/?i=inverse+%7B%7B2,4,0%7D,%7B6,1,2%7D,%7B1,1,4%7D%7D
http://www.wolframalpha.com/input/?i=%7B%7B2,4,0%7D,%7B6,1,2%7D,%7B1,1,4%7D%7D*%7B%7Bx%7D,%7By%7D,%7Bz%7D%7D+%3D+%7B%7B240%7D,%7B395%7D,%7B415%7D%7D
Mere, Sam and Nathan go to a bookshop to buy supplies for their school. Mere bought two erasers and four pencils and paid $2.40 for it. Sam bought six erasers, one pencil and two pens and paid $3.95 while Nathan paid $4.15 for an eraser, a pencil and four pens. Write a system of equations that can be used to find the cost of each item.Use the inverse matrix method to solve the system of equations.
[Hint: use Gauss Jordan elimination]
4 answers
cost of pencil --- p
cost of eraser --- e
cost of pen ----- x
2e + 4p = 2.4 (1)
6e + p + 2x = 3.95 (2)
e + p + 4x = 4.15 (3)
I would not use a matrix method, the equations are much too "nice".
from (1) : e = 1.2 - 2p
sub into (2)
6(1.2 - 2p) + p + 2x = 3.95
-11p + 2x = -3.25
2x = 11p - 3.25
4x = 22p - 6.5
now sub those into (3)
e + p + 4x = 4.15
1.2 - 2p + p + 22p - 6.5 = 4.15
21p = 9.45
p = .45
e = 1.2 - 2p = .30
x = 13.60
You can confirm my answer with this Gauss-Jordan applet
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
cost of eraser --- e
cost of pen ----- x
2e + 4p = 2.4 (1)
6e + p + 2x = 3.95 (2)
e + p + 4x = 4.15 (3)
I would not use a matrix method, the equations are much too "nice".
from (1) : e = 1.2 - 2p
sub into (2)
6(1.2 - 2p) + p + 2x = 3.95
-11p + 2x = -3.25
2x = 11p - 3.25
4x = 22p - 6.5
now sub those into (3)
e + p + 4x = 4.15
1.2 - 2p + p + 22p - 6.5 = 4.15
21p = 9.45
p = .45
e = 1.2 - 2p = .30
x = 13.60
You can confirm my answer with this Gauss-Jordan applet
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
Looks like I messed up for my x
I multiplied 4x by 4 instead of dividing by 4
4x = 3.4
x = .85
see Steve's solution
I multiplied 4x by 4 instead of dividing by 4
4x = 3.4
x = .85
see Steve's solution
DEAR SIR I NEED THE ANSWER OF THIS QUESTION PLEASE.Mere, Sam and Nathan go to a bookshop to buy supplies for their school. Mere bought
two erasers and four pencils and paid $2.40 for it. Sam bought six erasers, one pencil and
two pens and paid $3.95 while Nathan paid $4.15 for an eraser, a pencil and four pens.
a) Write a system of equations that can be used to find the cost of each item.
b) Use an appropriate method to solve the system of equations
two erasers and four pencils and paid $2.40 for it. Sam bought six erasers, one pencil and
two pens and paid $3.95 while Nathan paid $4.15 for an eraser, a pencil and four pens.
a) Write a system of equations that can be used to find the cost of each item.
b) Use an appropriate method to solve the system of equations
2 answers