SOLUTION: I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know?

Question 223231: I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know?

Here's an example:

Donnie has $5.10 in nickels, dimes, and quarters. He has an equal number of dimes and nickels, with the value of the quarters being $2.40 more than the total value of the dimes and nickels. How many dimes does he have?

Step 1. Let x be the number of nickels

Step 2. Let x be the number of dimes since they are equal in number with the nickels.

Step 3. Let be the dollar values of nickels and dimes.

Step 4. Let 0.25y be the dollar values of quarters.

Step 5. since the value of the quarters being $2.40 more than the total value of the dimes and nickels. Or rewriting it as

Step 6. Also, as given by the problem since $5.10 in nickels, dimes, and quarters.

Step 7. Now, we have a linear system of equations in Steps 5 and 6

Equation A
Equation B

Adding Equations A and B

quarters

Then solving x from Equation B is or .

Check Equation A if true or ...which is a true statement.

Step 8. ANSWER: The number of nickels and dimes is 9 each and the number of quarters is 15.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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