Question

The cost of 2 pencils and 5 pens together is rupees 31 and the cost of 5 pencils and 2 pens is rupees 25. Find the total cost of one pen and one pencil. *

Answer 1

Answer:

pencils = x

pens= y

2x+5y=31

2x=31-5y

x=31-5y/2.

5x+2y=25

5(31-5y/2)+2y=25

155-25y+4y=50

-21y=50-155

-21y=-105

y=-105/-21

y=5

x=31-5(5)/2

x=31-25/2

x=6/2

x=3

Answer 2

Answer

Step-by-step explanation

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The cost of 2 pencils and 5 pens together is Rs.31

• The cost of 5 pencils and 2 pens is Rs. 25

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The total cost of one pencil and one pen

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Let the cost of a pencil be x

Let the cost of pen be y

According to the given question:-

2 pencils + 5 pens = Rs.31

2x + 5y = 31 ...........(i)

5 pencils + 2 pens = Rs.25

5x + 2y = 25 ..........(ii)

Now we have the equations:-

2x + 5y = 31 ...........(i)

5x + 2y = 25 ..........(ii)

Multiply equations(i) with 5 and equation (ii) with 2

5( 2x + 5y = 31)

= 5(2x) + 5(5y) = 5(31)

= 10x + 25y = 155...........(iii)

2(5x + 2y = 25)

= 2(5x) + 2(2y) = 2(25)

= 10x + 4y = 50..............(iv)

By solving equations (iii) and (iv)

10x + 25y = 155

-10x + -4y = -50

____________

0 + 21y = 105

$\implies21y = 105 \\ \\ \implies y = \frac{105}{21} \\ \\ \implies y = 5$

Substituting y = 5 in equation (i)

$2x + 5y = 31 \\ \\ \implies2x + 5(5) = 31 \\ \\ \implies2x + 25 = 31 \\ \\ \implies2x = 31 - 25 \\ \\ \implies 2x = 6 \\ \\ \implies x = \frac{6}{2} = 3$

Therefore:-

The cost of pencil = x = Rs.3

The cost of pen = y = Rs. 5