The cost of 4 L of oil and 50 L of gasoline is $42.50. The cost of 3 L of oil and 35 L of gasoline is $30.30.

Question

The cost of 4 L of oil and 50 L of gasoline is $42.50. The cost of 3 L of oil and 35 L of gasoline is $30.30. Determine the cost of oil and 1 L of gasoline.

Answer 1

use a simultaneous equation

o = 1 letre of oil - Dont mix up with 0!!!
G = 1 letre of gasoline

4o + 50G = 42.50
3o + 35G = 30.30

Oil is 2.75$/L and Gas is 0. 63$/L

Thats how you work it out, ill have a go but im no good at maths,

inside the """ is where I changed the equasion.

4o + 50G = 42.50 """ x 3""" = 12o + 150G = 127.5
3o + 35G = 30.30 """x -4""" = -12o - 140G = -121.2

cancel out the 12o because there is positive and negative you are left with:

150G = 127.5
140G = 121.2 (I x by -1)

Now take away from eachother

10G = 6.3

devide by 10

Gasoline = 63 cent per letre.

Now substatute that back in one of the equasions to get the answer of Oil.

3o + (35 x0. 63) = 30.30

3o + 22.05 = 30.30

take away 22.05 from both sides

3o = 8.25 //// I made a mistake here, pasted the wrong answer from google calc. :D

devide by 3

1 letre of oil is = 2.75

Im not sure if its right but that will give u an idea about the method

Answer 2

4O + 50 G = 4250

3O + 35G = 3030

O stands for Oil and G for gasoline. Let us remove the decimal point for now.

Multiply the first equation with 3 and the second by 4.

12O + 150G = 12750

12O + 140G = 12120

Subtracting second from first,

10G = 630

G = 63 and we need to divide this by 100 to get dollars. The cost of 1 liter of Gasoline is 0.63 dollars.

4O + 50 x 63 = 4250

4O = 4250 - 3150 = 1100

So, one liter of Oil costs 1100 / 4 = 275 cents or 2.75 dollars

So, here are the figures:

Oil costs 2.75 dollars and gasoline costs 0.63 dollars per liter.

Answer 3

solve 2 simultanious equations.

i = cost of 1 L of oil
g = cost of 1 L of gas

4i + 50g = 42.50
3i + 35g = 30.30

multiply to eq by 3 & bottom by 4 then subtract them

12i + 150g = 127.50
12i + 140g = 121.20
--------------------------------

10g = 6.30
g = $ 0.63 per gallon

plug g into first equation to get:
4i + 50g = 42.50
4i + 50(0.63) = 42.50
4i = 11
i = $ 11/4 per L = $ 2.75 /L

Answer 4

Let the cost of 1L of oil be x, and the cost of 1L of gasoline be y.

Therefore,
4x + 50y = 42.50
3x + 35y = 30.30

Solve the 2 quadratic equations to get the answer.