5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77. Find the total cost of 1 book and 2 pens.
Answers
Given: 5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77.
Solution:
Let the cost of a book be ₹ x and that of a pen be ₹ y . Then,
5x + 7y = 79 ………..… (1)
and, 7x + 5y = 77 ………..… (2)
Elimination method is used to solve this Linear pair of Equations:
On Multiplying equation (1) by 5 and equation (2) by 7 we obtain :
25 + 35y = 395 ………..… (3)
49x + 35y = 539 ………..… (4)
On Subtracting equation (3) from equation (4) we obtain :
49x + 35y = 539
25 + 35y = 395
(-) (-) (-)
------------------
24x = 144
x = 144/24
x = 6
Therefore, cost of a book = ₹ 6
On Putting x = 6 in equation (1) we obtain :
5x + 7y = 79
5 × 6 + 7y = 79
30 + 7y = 79
7y = 79 - 30
7y = 49
y = 49/7
y = 7
Therefore, cost of a pen = ₹ 7
Then, cost of 2 pens = 2 × 7 = ₹ 14
Now , total cost of 1 book and 2 pens = 6 + 14 = ₹ 20
Hence, the total cost of 1 book and 2 pens is ₹ 20.
Hope this answer will help you…
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Answer:
Step-by-step explanation:
Solution:-
Let the cost of 1 book be x.
And the cost of 1 pen be y.
According to the Question,
⇒ 5x + 7y = 79 ..... (i)
⇒ 7x + 5y = 77 ......(ii)
Multiplying both Eq (i) with 7 and Eq (ii) with 5, we get
35x + 49y = 553 ...(iii)
35x + 25y = 385 ...(iv)
Substracting both the Eq (iii) and (iv), we get
⇒ 24y = 168
⇒ y = 168/24
⇒ y = 7
Putting y's value in Eq (i), we get
⇒ x = 6
Cost of book = x = 6
Cost of pen = 2(7) = 14
Total cost = 6 + 14 = Rs. 20
Hence, the total cost of 1 book and 2 pens is Rs. 20.