Question

Question 1 (ii)
Form the pair of linear equations in the following problems, and find their solutions graphically.
5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.

Answer 1

Let cost of a pencil = Rs x
Cost of a pen = Rs y
5 pencils and 7 pens together cost Rs 50.
So we get;
5x + 7y = 50
Subtracting 7y both sides we get;
5x = 50 - 7y
Dividing by 5 we get;
$x=10-\frac{7y}{5}$
Putting value of y = 5 , 10 and 15 we get
$x=10-7\times \frac{5}{5}=10-7=3$
$x=10-7\times \frac{10}{5}=10-14=-4$
$x=10-7\times \frac{15}{5}=10-21=-11$
$\begin{array}{cccc}x& 3& -4& -11\\ y& 5& 10& 15\end{array}$
Given that 7 pencils and 5 pens together cost Rs 46.
7x + 5y = 46
Subtracting 7x both side we get,
5y = 46 – 7x
Dividing by 5 we get,
$y=\frac{46}{5}-\frac{7x}{5}$
y = 9.2 – 1.4x
Putting x = 0 , 2 and 4 we get,
y = 9.2 – 1.4 × 0 = 9.2 – 0 = 9.2
y = 9.2 – 1.4 (2) = 9.2 – 2.8 = 6.4
y = 9.2 – 1.4 (4) = 9.2 – 5.6 = 3.6
$\begin{array}{cccc}x& 0& 2& 4\\ y& 9.2& 6.4& 3.6\end{array}$
Graphical representation:

Therefore, cost of one pencil = Rs 3 and cost of one pen = Rs 5.