A man hires an Ola cab to cover a certain distance. The fare is Rs. 10 for first kilometre and Rs. 7 for subsequent kilometers. Taking total distance covered is x km also total fare is Rs. y.
a) Write a linear equation for this.
b) Represent the equation in its standard form.
c) If the man covers 16 km distance and gave Rs. 120 Cab driver said, "It is not the correct
amount," and returned him the remaining balance. Find the correct amount.
Answers
The linear equation for total distance covered (x km) and total fare (Rs. y) is y = 7x + 3
This linear equation in its standard form is 7x - y = -3
If the man covers 16 km distance, the correct amount = Rs. 115
Given:
i) The fare charges for ola cab is Rs. 10 for first kilometre and Rs. 7 for subsequent kilometers.
ii) Total distance covered is taken as x km also total fare is taken as Rs. y.
To find:
a) Write a linear equation for this.
b) Represent the equation in its standard form.
c) If the man covers 16 km distance and gave Rs. 120 Cab driver said, "It is not the correct amount," and returned him the remaining balance. Find the correct amount.
Solution:
a) It is given that Rs. 10 is charged for first kilometre and Rs. 7 for subsequent kilometers.
Therefore,
y = total fare = 10 (fare for first kilometre) + 7*(x - 1) (fare for remaining (x - 1) kilometres)
=> y = 10 + 7*(x - 1)
=> y = 10 + 7x - 7
=> y = 7x + 3
b) The standard form of a linear equation in 2 variable is given by Ax + By = C
Therefore, shifting the 7x term to lhs, we get
y - 7x = +3
Multiplying this equation by -1 on both sides, we get
(y - 7x)*(-1) = +3*(-1)
=> -y + 7x = -3
=> 7x - y = -3
which is the equation in its standard form.
c) If the man covers 16 km distance, x = 16
Substituting the value of x in the linear equation y = 7x + 3, we get
y = total fare = 7*16 + 3
=> y = 112 + 3
=> y = 115
Therefore, the correct amount is Rs. 115
Hence,
linear equation for x and y is y = 7x + 3
equation in its standard form is 7x - y = -3
the correct amount is Rs. 115
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