Creating a system of equations

In summary, Pat invested $1200.00 in two types of bonds, one with a 4% annual interest rate and the other with a 6% annual interest rate. After one year, her investment grew to $1255.00. Using a system of equations, it can be determined that she invested $850 in the first bond and $350 in the second bond. The equations used were 0.04x + 0.06y = 55 and x + y = 1200. However, the correct equations should be 1.04x + 1.06y = 1255 and x + y = 1200.
  • #1
nation_unknown
7
0
I would like to thank-you for taking the time to read the current problem that I am going through. I understand the system of equations concept well however in this particular question they ask for me to produce a system of equations from a certain situation and then solve it myself. Here is the problem:

Pat invested $1200.00 at the beginning of the year. She placed the money in two types of bonds: one paying interest at 4% per annum and the other paying 6% per annum. At the end of the year, Pat's investment had grown to a value of $1255.00. Pat had misplaced some of her records and was wondering how much she had invested in each type of bond. Using a system of equations, determine how much Pat had invested in each type of bond.

I have tried producing the answer to this question in many different ways, including marking the two different bonds as x and y, and then trying to figure out (x)0.04 and (y)0.06 and how they come together to equal $1255. However I can not seem to get the system right in order to answer the overall question. If someone could help me out with calculating the system for this question I would very much appreciate it :). Thank-you once again for all of your time.
 
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  • #2
You seem to be on the right track, perhaps you just missed a small detail along the way. :smile:

One equation should show that the interest Pat got from both bonds should equal the profit she had made that year, which is $55. Therefore:

0.04x + 0.06y = 55

The other equation should show that the sum of x and y should be $1200, because that is how much Pat had invested in total:

x + y = 1200

Now solve for x and y. :smile: I get x = $850 and y = $350.
 
  • #3
nation_unknown said:
I have tried producing the answer to this question in many different ways, including marking the two different bonds as x and y, and then trying to figure out (x)0.04 and (y)0.06 and how they come together to equal $1255.
That is incorrect, because 4% and 6% is just the profit from the bonds, not the total amount of money they would return. That should be 104% and 106%, so:

1.04x + 1.06y = 1255
 
  • #4
Thank-you very much for your help. I now totally understand the question. I am so bad at those word questions, I really need to do some work in that area. Thank-you so much for your time and help!
 

1. How do you create a system of equations?

To create a system of equations, you must have two or more equations with two or more variables. These equations can be linear, quadratic, or any other type. You can then solve the system by using substitution, elimination, or graphing methods.

2. Why is it important to create a system of equations?

Creating a system of equations allows us to model and solve real-world problems. It helps us find the values of multiple variables that satisfy multiple equations simultaneously. This is crucial in many fields such as science, engineering, and economics.

3. What are the different methods for solving a system of equations?

There are three main methods for solving a system of equations: substitution, elimination, and graphing. In substitution, one variable is isolated in one equation and then substituted into the other equation. In elimination, one variable is eliminated by adding or subtracting the equations. In graphing, the solution is found by finding the intersection point of the two equations on a graph.

4. Can a system of equations have more than one solution?

Yes, a system of equations can have one, infinite, or no solutions. If the equations are consistent, meaning they have at least one solution, the system can have one or infinite solutions. If the equations are inconsistent, meaning they have no solutions, the system will have no solutions.

5. How can I check if my solution to a system of equations is correct?

To check if a solution is correct, you can substitute the values of the variables into each equation and see if they satisfy the equations. If the values make the equations true, then the solution is correct. You can also graph the equations and see if the point of intersection matches the solution.

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