The distance travelled (D) by a car in miles when it uses more than 1 liter of fuel is given by D= x +kv, where v is the liters of fuel used, and x, and k are constants. If the car uses 4 liters of fuel to travel 53 miles and 8 liters of fuel to travel 101 miles, how much fuel in litres will the car require to travel 149 miles?a)10b)11c)12d)13e)14Correct answer is option 'C'. Can you explain this answer?

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The distance travelled (D) by a car in miles when it uses more than 1 liter of fuel is given by D= x +kv, where v is the liters of fuel used, and x, and k are constants. If the car uses 4 liters of fuel to travel 53 miles and 8 liters of fuel to travel 101 miles, how much fuel in litres will the car require to travel 149 miles?

a)
10
b)
11
c)
12
d)
13
e)
14

Correct answer is option 'C'. Can you explain this answer?

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The distance travelled (D) by a car in miles when it uses more than 1 ...

Given

D = x + kv, where
- D is the distance travelled and v is the liter of fuel used
- x and k are constants
Case-I:
- 4 liters of fuel used to travel 53 miles
Case-II:
- 8 liters of fuel used to travel 101 miles

To Find: Liters of fuel used to travel 149 miles?

So, in the context of the equation 149 = x +kv
We need to find the value of v

Approach

To find the liters of fuel used to travel 149 miles, we will need to find the values of x and k. Since there are 2 unknowns, we will need 2 equations.
Case-I: Using 4 liters of fuel to travel 53 miles
1. 53 = x +4k……(1)
Case-II: Using 8 liters of fuel to travel 101 miles
1. 101 = x + 8k….(2)
As we have 2 equations and 2 unknowns, we can find the value of x and k.

Working Out

(2) – (1), we have

4k = 48, i.e. k =12.

Substituting the value of k in (1), we have x = 5

Putting the values of x and k in the equation 149 = x+ kv, we have

149 = 5 +12v, i.e. v = 12 liters

Hence, it will require 12 liters to travel a distance of 149 miles.

Answer: C

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