If seven books and 5 pens cost Rs 410, whereas five books and seven pens cost Rs.334 then the cost of three books and four pens would be
a) Rs.135
b) Rs.145
c) Rs.255
d) Rs.198
Full solution please. with steps
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*grade 10th*
*Linear Equation In Two Variables*
Answers
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Let cost of one book = Rs x and cost of one pen = Rs y
So by condition 1
7x + 5y = 410 - - - - - - - (1)
By condition 2
5x + 7y = 334 - - - - - - - (2)
Multiplying both sides of Equation 1 by 7 we get
49x + 35y = 2870 - - - - - - (3)
Multiplying both sides of Equation 2 by 5 we get
25x + 35y = 1670 - - - - - - (4)
Equation 3 - Equation 4 gives
24x = 1200
⇒ x = 50
From Equation 1 we get
5y = 410 - 7x
⇒ 5y = 410 - ( 7 × 50 )
⇒ 5y = 410 - 350
⇒ 5y = 60
⇒ y = 12
∴ Cost of one book = Rs 50 and cost of one pen = Rs 12
Hence the required cost of three books and four pens
= Rs 3x + Rs 4y
= Rs 150 + Rs 48
= Rs 198
FINAL ANSWER
Hence the correct option is d) Rs. 198
Step-by-step explanation:
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