Question

The sum of the cost of one book each of math, physics and chemistry is ₹210. The total cost of a math book, 2 physics books and a chemistry book is ₹240. Also the total cost of a math book ,3 physics and chemistry book is ₹300. Find the cost of each math, physics and chemistry book using matrices.

Answer 1

Answer:

210/240/300*1*2*3=0.0175

Step-by-step explanation:

210/240/300*1*2*3=0.0175

Answer 2

Correct Question

The sum of the cost of one book each of math, physics and chemistry is ₹210. The total cost of a math book, 2 physics books and a chemistry book is ₹240. Also the total cost of a math book ,3 physics and 2 chemistry book is ₹300. Find the cost of each math, physics and chemistry book using matrices.

Answer:

The cost of each math, physics and chemistry book are Rs.150, Rs.30 and Rs.30 respectively.

Step-by-step explanation:

Given:

The sum of the cost of one book each of math, physics and chemistry is ₹210.

The total cost of a math book, 2 physics books and a chemistry book is ₹240.

The total cost of a math book ,3 physics and chemistry book is ₹300.

To Find:

The cost of each math, physics and chemistry book.

Solution:

Let cost of 1 math book,1 physics book and 1 chemistry  book are x,y and z respectively.

As given-the sum of the cost of one book each of math, physics and chemistry is ₹210.

$x+y+z=210$ ----- equation no.01.

As given-the total cost of a math book, 2 physics books and a chemistry book is ₹240.

$x+2y+z=240$    ------equation no.02.

As given-the total cost of a math book ,3 physics and chemistry book is ₹300.

$x+3y+2z=300$  --------- equation no.03.

Solving the equation no.01. equation no.02 and equation no.03 by using matrices.→

In matrix  form,

$\left[\begin{array}{ccc}1&1&1\\1&2&1\\1&3&2\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}210\\240\\300\end{array}\right]$

$R_{2}$→$R_{2} -R_{1}$  and $R_{3} =R_{3} -R_{1}$

$\left[\begin{array}{ccc}1&1&1\\0&1&0\\0&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}210\\30\\90\end{array}\right]$

$R_{3} =R_{3} -2R_{2}$

$\left[\begin{array}{ccc}1&1&1\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}210\\30\\30\end{array}\right]$

$\left[\begin{array}{c}x+y+z\\y\\z\end{array}\right] = \left[\begin{array}{c}210\\30\\30\end{array}\right]$

$x+y+z=210$  ------ equation 04.

$y=30$  and $z=30$.

Putting the value of y and z the equation no.04.

$x+y+z=210$

$x+30+30=210$

$x+60=210$

$x=150$

The cost of each math, physics and chemistry book are Rs.150, Rs.30 and Rs.30 respectively.

PROJECT CODE#SPJ2