Question

the cost of 7 pencils 5pens 2 books is rupees 39 the cost of 5 pencil 3 pens and 4 books is rupees 39 the cost of 3 pencils 5 men and 7 books is 56 find the cost of each pen

Answer 1

₹3 is the answer of the question

Answer 2

Heya!

Let, the cost of 1 pencil =x

the cost of 1 pen = y

the cost of 1 book = z

According to the Hypothesis,

7 pencils, 5 pens and 2 books costs Rs. 39

7x+5y+2z = 39 -----------(1)

5 pencils , 3 pens and 4 books costs Rs. 39

5x+3y+4z = 39 -----------(2)

3 pencils, 5pens and 7 books costs Rs.56

3x+5y+7z = 56 -----------(3)

From (1) and (2),

7x+5y+2z = 5x+3y+4z

7x-5x +5y-3y +2z -4z= 0

2x+2y-2z = 0

x + y -z = 0 ------(4)

From (3) and (4)

eq.(3) x 1

eq.(4) x 3

3x+5y+7z = 56

3x+3y -3z = 0

-- -- +

________________

2y+10z = 56

y+5z = 23 ----------(5)

Here, (18,1) ,(13,2),(8,15) and (3,4) are the values satisfied for..y and z of equation 5

But, only the value y = 3 and z = 4 satisfies the eq.(1) ,(2) and (3) and (4)

Therefore, y = 3

Hence, cost of each pen = Rs.3

Hope it helps..