The cost of dozen showpieces is Rs. 300.72. What will be the cost of one showpiece?
Answers
Answer:
Let the cost of one dozen pencils, one dozen pends and one dozen erasers be Rs.x,Rs.y and Rs.z respectively.
According to the questions,
4x+3y+2z=60
2x+4y+6z=90
6x+2y+3z=70
The above equations can be expressed in the matrix form as
⎣
⎢
⎢
⎡
4
2
6
3
4
2
2
6
3
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
60
90
70
⎦
⎥
⎥
⎤
Using R
2
→R
2
−
2
1
R
1
and R
3
→R
3
−
2
3
R
1
⎣
⎢
⎢
⎢
⎢
⎢
⎡
4
0
0
3
2
5
−
2
5
2
5
0
⎦
⎥
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
60
60
−20
⎦
⎥
⎥
⎤
Using R
3
→R
3
+R
2
, we get
⎣
⎢
⎢
⎢
⎡
4
0
0
3
2
5
0
2
5
5
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
60
60
40
⎦
⎥
⎥
⎤
Now the equations can be rewrite in their original form as
5z=40....(i)
⇒z=8
2
5
y+5z=60....(ii)
4x+3y+2z=60....(iii)
Putting the value of z in equation (ii),
2
5
y+5(8)=60
y=
5
(60−40)
×2=8
⇒y=8
Putting the values of y and z in equations (iii), we get
4x+3(8)+2(8)=60
4x=60−24−16
x=
4
20
=5
∴x=5
∴ The cost of each item per dozen are Rs.5,Rs.8 and Rs.8 respectively.