Question

(ii) 5 pencils and 7 pens together cost ` 50, whereas 7 pencils and 5 pens together

cost ` 46. Find the cost of one pencil and that of one pen.

Answer 1

let the cost of 1 pencil =rs x
let the cost of 1 pen =rs y
by A.T.Q
5x+7y=50..............i
7x+5y=46............ii
multiplying eq i by 5 and ii by 7;we get
25x+35y=250.....iii
49x+35y=322....iv
on subtracting eq. iii from iv
24x=72
x=72/24
x=3

Answer 2

Answer:

Answer:-

$\red{\bigstar}$ Cost of 1 pencil

$\large\leadsto\boxed{\sf\purple{Rs. \: 3}}$

$\red{\bigstar}$ Cost of 1 pen

$\large\leadsto\boxed{\sf\purple{Rs. \: 5}}$

• Given:-

Cost of 5 pencils and 7 pens = Rs. 50

Cost of 7 pencils and 5 pens = Rs. 46

• To Find:-

Cost of 1 pencil and 1 pen = ?

• Solution:-

Let the price of pencil be 'x' and the price of pen be 'y'.

According to the question:-

→ $\sf{5x + 7y = 50} \: \: \: \longrightarrow\bf\red{[eqn.i]}$

and

→ $\sf{7x + 5y = 46} \: \: \: \longrightarrow\bf\red{[eqn.ii]}$

Multiplying eqn[i] by 5:-

→ $\sf{(5x + 7y = 50) \times 5}$

→ $\sf{25x + 35y = 250}\: \: \: \longrightarrow\bf\red{[eqn.iii]}$

Multiplying eqn [ii] by 7:-

→ $\sf{(7x + 5y = 46) \times 7}$

→ $\sf{49x + 35y = 322}\: \: \: \longrightarrow\bf\red{[eqn.iv]}$

Subtracting equation [iii] from [iv]:-

→ $\sf{(49x + 35y) - (25x + 35y) = 322 - 250}$

→ $\sf{49x + 35y - 25x - 35y = 72}$

→ $\sf{24x = 72}$

→ $\sf{x = \dfrac{72}{24}}$

→ $\boxed{\bf\green{x = 3}}$

Substituting value of x in [eqn.i]:-

→ $\sf{5x + 7y = 50}$

→ $\sf{5 × 3 + 7y = 50}$

→ $\sf{15 + 7y = 50}$

→ $\sf{7y = 50 - 15}$

→ $\sf{7y = 35}$

→ $\sf{y = \dfrac{35}{7}}$

→ $\boxed{\bf\green{y = 5}}$

Therefore,

The cost of 1 pencil is Rs. 3

The cost of 1 pen is Rs. 5