Question

the taxi fare in a city is such that rs 8 for first kilometers namaste and for the the subsequent distance it is rs 5 per km. write a linear equation to represent this information in two variables taking distance covered as x km and total fare as y.what will be the distance travelled by a person if he spent rs 63​

Answer 1

Working out:

It is said that, there is a fixed charge for the first kilometre i.e. Rs. 8 and an additional charge per km thereafter i.e Rs. 5.

Let,

• Total distance covered be x
• Total fare taken is y

According to question, the person have to pay Rs.8 for first 1 km, and then Rs.5 for rest kms each.

⇛ Total fare = Charge for 1 km + Subsequent charge × No. of Kms left.

Plug the values given,

⇛ y = 8 + 5(x -1)

⇛ y = 8 + 5x - 5

⇛ y = 5x + 3

Hence,

• 5x + 3 is the required linear equation.✓

Now we are given with the total fare of a person who has travelled some distance. The total fare is Rs. 63

⇛ y = Rs. 63 (Total fare)

And, we have already derived the linear equation which establish the relation between Total fare and Kms travelled.

We have y, So let's find x

⇛ y = 5x + 3

⇛ 63 = 5x + 3

⇛ 60 = 5x

⇛ x = 12

Hence,

• The total distance travelled = 12 km✓

And, we are done !$!$

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Answer 2

$\sf \purple{Let:-}$

• Total distance covered as 'x'
• Total fare taken as 'y'

$\sf \purple{According \: To \: Question:-}$

• A person will.have to pay Rs 8 for 1 km.
• Then Rs 5 for next covered kms.

$\sf \purple{Formula:-}$

➡️ Total fare:-

Charge for 1 km + Subsequent charge × No. of Kms left.

$\sf \purple{Enter \: all \: values}$

$\implies\mathtt{y = 8 + 5(x -1)}$

$\implies \mathtt{y = 8 + 5x - 5</p><p>}$

$\implies\mathtt{y = 5x + 3}$

$\sf \red{Hence,}$

• 5x + 3 is the required linear equation.
• Now we are given with the total fare of a person who has travelled some distance.
• The total fare is Rs. 63

$\implies \mathtt{y = Rs. 63 (Total \: fare)}$

• And Yes, we have already derived the linear equation which establish the relation between Total fare and Kms travelled.

We have 'y', So let's find 'x'

$\implies \mathtt{y = 5x + 3}$

$\implies \mathtt{63 = 5x + 3}$

$\implies \mathtt{60 = 5x}$

$\implies \mathtt{x = 12}$

So the total distance travelled is:-

${ \boxed{ \mathtt{\red{12 \: km}}}}$