Question

The price of 9 pencils and 12 pens is₹279 and that of 8 pencils and 16 pens is ₹312.Then sum of the cost of one pen and a pencil is​

Answer 1

Step-by-step explanation:

Given :-

The price of 9 pencils and 12 pens is₹279 and that of 8 pencils and 16 pens is ₹312.

To find :-

Find the sum of the cost of one pen and a pencil?

Solution :-

Let the cost of one pencil be ₹ X

Let the cost of one pen be ₹ Y

Given that

The price of 9 pencils and 12 pens = ₹ 279

=> 9X+12 Y = 279

=> 3(3X+4Y) = 279

=> 3X+4Y = 279/3

=> 3X+4Y = 93 --------------(1)

And

The cost of 8 pencils and 16 pens = ₹ 312

=> 8X +16Y = 312

=> 8(X+2Y) = 312

=> X+2Y = 312/8

=>X+2Y = 39 ---------------(2)

=> X = 39-2Y -------------(3)

On Substituting the value of X in (1) then

3X+4Y = 93

=> 3(39-2Y) +4Y = 93

=> 117-6Y+4Y = 93

=> 117-2Y = 93

=> -2Y = 93-117

=> -2Y = -24

=> Y = -24/-2

=> Y = 12

On Substituting the value of Y in (3)

=> X = 39-2(12)

=> X = 39-24

=> X = 15

Therefore X = 15 and Y = 12

The cost of one pencil =₹15

The cost of one pen = ₹ 12

Now ,

The sum of the cost of one pencil and the cost of one pen

=> 15+12

= ₹ 27

Answer:-

The sum of the cost of one pencil and the cost of one pen = ₹ 27

Check:-

The cost of one pencil =₹15

The cost of one pen = ₹ 12

The price of 9 pencils and 12 pens

=> 9(15)+12(12)

=> 135+144

= 279

and

The cost of 8 pencils and 16 pens

=> 8(15)+16(12)

=> 120+192

=> 312

Verified the given relations in the given problem.

Used Method :-

• Substitution method

Answer 2

Given:-

• The price of 9 pencils and 12 pens is₹279 and that of 8 pencils and 16 pens is ₹312.

To Find:-

• Sum of the cost of one pen and a pencil.

Method Used:-

• Substitution Method

Solution:-

Let the cost of 1 pencil be x and the cost of 1 pen be y.

According to question,

$:\implies\:9x + 12y = 279$

$:\implies\:3x + 4y = 93$ ____{1}

Also,

$:\implies\:8x + 16y = 312$

$:\implies\:2x + 4y = 78$ ____{2}

Subtracting {2} from {3},

⠀⠀⠀⠀⠀ $\bf 3x + 4y = 93$

⠀⠀⠀⠀⠀ $\bf 2x + 4y = 78$

⠀⠀⠀ (–)⠀ ⠀(–)⠀ ⠀(–)

⠀⠀⠀⠀━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀ $\bf x = 15$

Putting Value of x in {1},

$:\implies\:3\times15 + 4y = 93$

$:\implies\:45 + 4y = 93$

$:\implies\:4y = 93-45$

$:\implies\:4y = 48$

$:\implies\:y = \dfrac{48}{4}$

$:\implies\:y = 12$

The value of x and y is 15 and 12 respectively.

• Cost of 1 pencil = x = ₹15

• Cost of 1 pen = y = ₹12

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