Creating a system of equations

[nation_unknown]

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.

 

[Chen]

You seem to be on the right track, perhaps you just missed a small detail along the way.

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. I get x = $850 and y = $350.

 

[Chen]

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

 

[nation_unknown]

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!