Question

Two pens and one eraser Cost 35 and 3 pencils and four erasers cost 65. FIND the cost of a pencil and eraser separately

Answer 1

Let the cost of one pencil be x

and that of eraser be y

By question,

2x+y=35 ....... 1

3x+4y=65 ....... 2

Multiplying equation 1 with 4

8x+4y= 140

-3x_+4y=-65

5x=75

x=75/5

x=15Rs

Therefore 3*15+4y=65

4y=65-45

y=20/4

y=5Rs

Therefore cost of pencil is 15Rs and cost

of eraser is 5 Rs

Answer 2

Cost of a pencil is Rs. 15 and cost of one eraser is Rs. 5.

Given :

• Cost of two pencils and one eraser is 35, and
• Cost of three pencils and four erasers are 65.

To find:

• Find the cost of one pencil and one eraser.

Solution:

Concept to be used:

1. Assume the cost of single pencil and single eraser as variables.
2. Write equations from the statement.
3. Solve equations to find the cost separately.

Step 1:

Write the equations.

Let the cost of one pencil is 'x' rupees and cost of one eraser is 'y' rupees.

ATQ

$\bf 2x + y = 35...eq1 \\ \bf 3x + 4y = 65...eq2$

Step 2:

Solve the equations.

Multiply eq1 by 4 and subtract both equations.

$8x + 4y =14 0 \\ 3x + 4y = 65 \: \: \\ ( - ) \: \: ( - ) \: \: ( - ) \\ - - - - - - - - \\ 5x = 75 \\ - - - - - - - -$

or

$x = \frac{75}{5}$

or

$\bf \red{x = 15}$

Put the value of x in eq1 and find the value of y.

$2(15)+ y = 35$

or

$y = 35 - 30$

or

$\bf \red{y = 5}$

Thus,

Cost of a pencil is rupees 15 and cost of one eraser is rupees 5.

#SPJ3

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