Question

Unleaded gas and supreme gas sell for different prices per liter. Suppose that 2 liters of unleaded gas and 3 liters of supreme gas cost a total of $2.52. Five liters of unleaded gas and 4 liters of supreme gas cost a total of $4.48. What is the price per liter of each kind of gas? If Ted filled his pickup with 30 liters of unleaded gas and Rachel filled her car with 25 liters of supreme gas, how much would they collectively have to pay for the gas? Assume prices have not changed.

Answer 1

Given:

Unleaded gas and supreme gas sell for different prices per litre. Suppose that 2 litres of unleaded gas and 3 litres of supreme gas cost a total of $2.52. Five litres of unleaded gas and 4 litres of supreme gas cost a total of $4.48.

To Find:

What is the price per litre of each kind of gas? If Ted filled his pickup with 30 litres of unleaded gas and Rachel filled her car with 25 litres of supreme gas, how much would they collectively have to pay for the gas? Assume prices have not changed.

Solution:

First, we would need to formulate the linear equation, let the variable for unleased gas be x and for supreme gas be y, now using the given situation we have,

$2x+3y=2.52$     -(1)

The second equation will be using the same process,

$5x+4y=4.48$    -(2)

Now multiply equation 1 with 5 and equation 2 with 2, we have,

$10x+15y=12.6\\10x+8y=8.96$

Now subtracting both the equation with each other, we have

$7y=3.64\\y=0.52$

So y is $0.52 and putting y=0.52 in equation 1 we get the value of x as,

$2x+3*0.52=2.52\\x=0.48$

So the value of x is $0.48.

Now if Ted filled 30L of unleaded gas and Rachel filled 25L of supreme gas then the collective amount they will pay is,

$Total cost=30x+25y\\=30*0.48+25*0.52\\=27.6$

Hence, the price per litre of unleased gas is $0.48 and of supreme gas is $0.52 and the collective they have to pay is $27.6