3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324. Find the total cost of 1 bag and 10 pens.
Answers
Given : 3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324.
Solution:
Let the cost of a bag be ₹ x and that of a pen be ₹ y. Then,
3x + 4y = 257 ………..… (1)
4x + 3y = 324 …...… (2)
Elimination method is used to solve this Linear pair of Equations:
On Multiplying equation (1) by 3 and equation (2) by 4, we obtain :
9x + 12y = 770 ………..… (3)
16x + 12y = 1296 ………..… (4)
On Subtracting equation (3) from equation (4) we obtain :
16x + 12y = 1296
9x + 12y = 770
(-) (-) (-)
------------------
7x = 525
x = 525/7
x = 75
Cost of a pen = ₹ 75
On Putting x = 75 in equation (1) we obtain :
3x + 4y = 257
3 × 75 + 4y = 257
225 + 4y = 257
4y = 257 - 225
4y = 32
y = 32/4
y = 8
Therefore, Cost of a pen = ₹ 8
then, Cost of 10 pens = 8 × 10 = ₹ 80
cost of 1 bag and 10 pens = 75 + 80 = ₹ 155.
Hence, the total cost of 1 bag and 10 pens is ₹ 155.
Hope this answer will help you…
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Let the cost of a bag be Rs x and that of a pen be Rs y . Then,
3x+4y=257 .........(i)
4x+3y=324 .........(ii)
Multiplying equation (i) by 3 and equation (ii) by 4, we get
9x+12y=771 .......(iii)
16x+12y=1296 ........(iv)
Subtracting equation (iii) by equation (iv), we get
16x-9x = 1296-771
7x. = 525
x = 525/7
x = 75
cost of one bag = ₹75
putting x= 75 in equation (i) we get
3×75 + 4y = 257
225+ 4y = 257
4y = 257 - 225
4y = 32/4
y = 8
therefore,
cost of a pen = ₹8
& cost of 10 pen = 10× ₹8
= ₹80
Hence, the total cost of 1 bag and 10 pens = 75+80 = Rs 155.