5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of 1 pen and 1 pencil.
Answers
Given : 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5.
Solution:
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
5x + 6y = 9 ……..…(1)
3x + 2y = 5 ………..(2)
On Multiplying equation(1) by 2 and equation (2) by 6, we obtain :
10x + 12y = 18 ……..…(3)
18x + 12y = 30 ……..…(4)
On Subtracting equation(3) by equation(4), we obtain :
18x + 12y = 30
10x + 12y = 18
(-) (-) (-)
-----------------
8x = 12
x = 12/8
x = 3/2
On Substituting x = 3/2 in equation (1), we get
5x + 6y = 9
5 × 3/2 + 6y = 9
15/2 + 6y = 9
6y = 9 - 15/2
6y = (18 - 15)/2
6y = 3/2
y = 3/2 × ⅙
y = ¼
Hence, cost of one pen is Rs. 3/2 and cost of one pencil is Rs. ¼.
Hope this answer will help you…
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