proportion problem type 2

Question

Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains
7
liters of natural oil for every
5
liters of synthetic oil. In order to make
1152
liters of Petrolyn oil, how many liters of natural oil are needed?

Answer 1

This problem covers two topics: proportions and systems of equations.

 

Let x represent the amount of liters of natural oil

Let y represent the amount of liters of synthetic oil

 

Because there are always 7 liters of natural oil for every 5 liters of synthetic oil, we can write the proportion:

         

                      7/5 = x/y

 

With this proportion, we can cross-multiply to achieve the equation: 

 

                     7y = 5x                            (1)

 

This is where we bring in another equation and establish the system of equations portion of the problem.

We know that the total amount of Petrolyn oil is the sum of the amount of natural oil and synthetic oil. So,

 

                     x + y = 1152                   (2)

 

We are only concerned about the amount of natural oil that is needed, which is represented by x. So, we can solve equation (1) for y, and substitute it in equation (2). 

Solve equation (1) for y by dividing both sides by 7:

 

                    y = (5x)/7 

 

Now, substitute this into equation (2):

 

                    x + (5x)/7 = 1152

 

Now that x is our only remaining variable, we can solve for it:

 

                   (7x)/7 + (5x)/7 = 1152                       (need common denominators to add fractions)

 

                   (12x)/7 = 1152                                   (add the fractions)

 

                   12x = 8064                                        (multiply both sides by 7)

 

                    x = 672                                             (divide both sides by 12)

 

Therefore, in a mix of 1152 liters of Petrolyn oil, there are 672 liters of natural oil. 

 

-Ray Biggerstaff 

 

                   

 

 

 

 

 

 

 

 

Answer 2

7 liters of natural oil and 5 liters of synthetic oil constitutes every (7+5) or 12 liters of Petrolyn motor oil

or                                       

                               every 12 liters of Petrolyn motor oil contains 7      liters of natural oil and 5   liters of synthetic oil

Hence, by law of proportions,

                                   each liters of Petrolyn motor oil contains 7/12 liters of natural oil and 5/12 liters of synthetic oil 

Therefore, by law of proportions,
1152, liters of Petrolyn motor oil contains [(7/12)*1152] liters of natural oil and[(5/12)*1152] liters of synthetic oil

=>1152, liters of Petrolyn motor oil contains 672  liters of natural oil and 480 liters of synthetic oil

 

Thus, in order to make 1152, liters of Petrolyn motor oil 672 liters of natural oil are needed.

Answer 3

To solve this problem, we need to figure out what proportion we are trying to set up.  The problem is asking for liters of natural oil and we are given total liters of Petrolyn oil. We can write this information as a proportion as follows:

 

x liters Natural / 1152 liters Petrolyn.

 

The other given information is that Petrolyn is made up of 7 liters Natural to 5 liters Synthetic.  From this we can deduce that a batch of Petrolyn contains 12 liters (7 + 5 = 12).  With this we can create a proportion for Natural oil to Petrolyn oil as follows:

7 liters Natural / 12 liters Petrolyn

 

Using both proportions, we can solve for x

 

7 Liters Natrual     =     x Liters Natural

      12 Liters Petrolyn        1152 Liters Petrolyn

 

  (1152 * 7)  =   (12 * x)

         8064   =   12x

            672  =  x

 

So we need 672 Liters of Natural oil to make 1152 Liters of Petrolyn.

 

We can double check this by figuring out how many liters of Synthetic oil would be used with 672 liters of natural oil and adding the answers together.

 

7 Liters Natural    =    672 Liters Natrual

5 Liters Sythetic          x Liters Synthetic 

 

(7*x)   =   (5*672)

     7x  =  3360

      x   =  480

480 + 672  =  1152