Question

A motorist buys 24 litres of petrol and litres of oil for $10.70, while another motorist buys 18 litres of petrol and 10 litres of oil for $12.40. Find the cost of 1 litre of petrol and 1 litre of oil at this garage.

Answer 1

The cost of 1 litre of petrol is $ 0.3 and 1 litre of oil is $0.7 at this garage.

• In mathematics, linear equations are those in which the variable's maximum power is one. A straight line is the only possible solution to a linear equation. Thus, a system of two linear equations in two or three variables that are solved simultaneously to arrive at a shared solution is known as a simultaneous linear equation.
• The simultaneous linear equations are often solved using three different approaches. They are: the Graphical Method, the Elimination Method, and the Substitution Method.

Here, according to the given information, it is given that,

A motorist buys 24 litres of petrol and 5 litres of oil for $10.70.

Let there be x litres of petrol and y litres of oil.

Then, for the first motorist, we have,

24x + 5y = 10.70 ...(1)

Again, it is given that, another motorist buys 18 litres of petrol and 10 litres of oil for $12.40.

Then, we have,

18x + 10y = 12.40 ...(2)

Now, we need to solve the system of simultaneous linear equations to get the values of x and y.

Now, solving equations (1) and (2), we get,

Multiplying (1) by 2 and (2) by 5, we get,

240x + 50y = 107 ...(3)

90x + 50y = 62 ...(4)

Subtracting (4) from (3), we get,

150x = 45

Or, x = 0.3

Now, putting the value of x in equation (2), we get,

18(0.3) + 10y = 12.40

Or, 10y = 12.40 - 18(0.3)

Or, y = 0.7

Hence, the cost of 1 litre of petrol is $ 0.3 and 1 litre of oil is $0.7 at this garage.

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