Question

petroleum motor oil is a combination of natural oil and synthetic oil. it contains 7 liters of natural oil for every 4 liters of synthetic oil. in order to make 594 liters of petroleum oil, how many liters of natural oil are needed? liters of natural oil

Explanation:

Step1: Set up the ratio - based equation

Let the number of sets of the ratio be $x$. The ratio of natural oil to synthetic oil is $7:4$. The total volume of the motor - oil combination is the sum of natural and synthetic oil. So the total volume of one set of the ratio is $7 + 4=11$ liters.

Step2: Find the number of sets

We know the total volume of the motor oil is 594 liters. Since the volume of one set of the ratio is 11 liters, we can find the number of sets $x$ by dividing the total volume by the volume of one set. So $x=\frac{594}{11}=54$.

Step3: Calculate the volume of natural oil

Since there are 7 liters of natural oil in each set, and the number of sets is 54, the volume of natural oil is $7\times54 = 378$ liters.

Answer:

378 liters