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Question
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
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Solution
Let the fixed charge for the first three days and each day charge thereafter be Rs x and Rs y, respectively.
According to the question,
x + 4y = 27 ...(1)
The charge for keeping a book for five days is ₹ 2.
x + 2y = 21 ...(2)
By subtracting equation (2) from equation (1)
(x + 4y = 24) - (x + 2y = 21)
y = 3
Putting the value of y in equation (1)
x = 15
Hence, the fixed charge is ₹ 15 and the charge for the additional day is ₹ 3.
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