Use a system of linear equations to solve Exercises 73–84. How ma...

Question

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?

Accepted Answer

Welcome back. I am so glad you're here. We have a student doing an experiment in the laboratory and we need to figure out how many military leaders of a solution they are using. So we're going to let that unknown amount B X. That's however many milliliters and we have some more information about that. We know that it is milliliters of a 12% acid solution. So we can say that that is 120. X. And it's getting combined with so it's being added to 250 mL of a 24% acid solution. 24% asset solution would be . times the amount of liquid there. Well, we know this amount that's not unknown. This one is 250 milliliters And together they will be combined to produce to equal a 15% acid solution. So that's going to be .15 for the 15%. And how much of that liquid is there going to be? Well, there's going to be our mystery amount are unknown X plus the 250 that we do know about. And that is how much of the 15% acid solution there will be And now the only variable here is X. And we can solve for X. We just need to do the math. So bringing down that 150.12 X plus multiplying .24 times 250 will give us 60 equals and distributing that 0.15. So 0.15 times X is 0.15 X and 0.15 times 250 is plus 37.5. Now we can combine like terms, let's bring this 0.12 X over to the right hand side, oops. And let's bring this 37.5 over to the left hand side. So on the left 60 minus 37.5 is 22.5 equal to 0. minus 0.12 is 0.3 X. Now we'll divide both sides by 0. And we'll get a solution of x equals 22.5 divided by .03 is 750 so it is ml of That 12% acid solution that the student is using. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?

Key Concepts

Linear Equations

Concentration and Mixture Problems

System of Equations

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