how many liters of Petrolyn oil will be made?

Question

Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 3 liters of synthetic oil. If 243 liters of natural oil are used, how many liters of Petrolyn oil will be made?

Answer 1

Petrolyn (P) is made up of 4 parts Natural oil (N) and 3 parts Synthetic oil (S), which equals 7 parts total. (4+3=7)

 

So then the equation is: P = 4/7N + 3/7S

 

The problem is how much P is made when using 273 liters N.

 

Assuming we are using enough synthetic to combine with all 273 liters of natural oil, the equation is:

 

4/7P = 273

(because we know how much N we have, and the total volume (P) is comprised of four sevenths (4/7) natural oil (N).

 

if we invert and multiply, we get:

 

P = 273 x 7/4 = 425.25 (rounding down to 425)

 

We can think about it another way:

 

Algebraically, the problem is represented as:

 

4x + 3x = P, where 4x = 243 (solve for x, x = 60.75)

 

Substitute:

 

243 + 3(60.75) = P

 

243 + 182.25 = P

 

P = 425.25 (rounding down to 425)

 

To check this, we can substitute in the original ratio, which is 4 + 3 = 7 (4 L Natural and 3 L Synthetic)

 

If our math is right we should end up with P = 7

 

4 x 7/4 = 7

 

and

 

4 + 3(1) = 7

 

Answer 2

ratio of synthetic to natural = 3/4

3/4 = s/243         multiply both sides by 243

(243)(3)/4 = s

182.25 = s

 

 

Amount of Petrolyn = 243 + 182.25, or 425.25 L