# 5 pencils &7 pens together cost Rs.50 whereas 7 pencils & 5 pens together costs Rs. 46.find the cost of one pen & one pencil

2
by vishn

2015-05-12T21:44:58+05:30
Let cost of a pen be x and cost of pencil be y
acc. to first statement , 5y+7x=50_______(1)
rearranging equation, we get, x=(50-5y)/7
acc to second statement , 7y+5x=46---------(2)
substituting value of x in 2 ,
7y+5(50-5y)/7 = 46
solving the equation we get , y=3 and x=5
hence cost of one pen is 5 rs. and cost of one pencil is 3 rs.
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2015-05-13T01:08:02+05:30
Let the cost of the pencil be x and pen be y
5 pencils &7 pens together cost Rs.50
i.e., 5x+7y = 50 ------ 1
7 pencils & 5 pens together costs Rs. 46
i.e., 7x+5y = 46 ------- 2

now,
multiply 1st equation with 7 and 2nd equation with 5 in order to cancel a pair of similar terms

eqn 1 × 7 i.e.,  7( 5x+7y = 50 )
35x+49y = 350 -------- 3
eqn 2 × 5 i.e.,   5( 7x+5y = 46 )
35x+25y = 230 -------- 4

now subtract eqn 4 from eqn 3

35x+49y = 350
35x+25y = 230
-       -         -
--------------------------------
24y = 120
--------------------------------
y = 120/24
y = 5
therefore, cost of the pen (y) = 5 Rs

substitute  y=5 in eqn 1. 5x+7y = 50
5x+7(5) = 50
5x = 50 - 35
5x = 15
x = 3
therefore, cost of the pencil (x) = 3 Rs

Hence: Cost of each pen (y) is Rs. 5 and cost of each pencil (x) is Rs. 3

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