First I am suppose to solve this problemsystems by using the

First, I am suppose to solve this problem/systems by using the elimination method. I dont understand how there are two systems with the below probelm. The problem is: Solve the following application problem usig the elimination method. Two different gasohol mixtures are available. One Mix contains 4% alcohol and the other, 12% alcohol. How much of each mixtures should be used to get 20,000 L of gasohol cotaining 9% alcohol?

The questions I would like answered if possible:

1) Is there a way to make this into a two equation system in order to apply the elimination method?

2) Which of the two set ups is correct if at all?

3) Is the correct set up executed correctly?

Result 1:

X(.04) + X(.12) = 20000(.09)

                .16X = 20000(.09)

                .16X = 1800

          .16/.16X = 1800/.16

                     X = 11250 L

Answer : 450 L of 4% alcohol and 1350 L of 12% alcohol

Result 2:

X(.04) + X(.12) = 20000

                .16X = 20000

          .16/.16X = 20000/.16

                     X = 125000 L of each mixture

Answer : 5000 L of 4% alcohol and 1500 L of 12% alcohol

Thanks!

Solution

Given : Two different gasohol mixtures are available. One Mix contains 4% alcohol and the other, 12% alcohol.

We need to assume two diiferent variables for two types of gasohol mixture

Lets take 4% alcohol as x litres and 12% alcohol mixture as y lites

We need to have two equations with two variables to have sa syetm of equations:

X(.04) + Y(.12) = 20000(.09) ----(1)

Total volume of mixture after mixing two different types of mix is 20000 litres

X +Y = 20,000   -----(2)

We have two equations (1) and (2) we can solve by elimination method

So you can understand the mistake in your solution