Algebra Word Problem: Investment Amounts

[Mack2002]

Not sure how to start this one: Yolanda invests \$6000. Some of the money is invested in stocks paying 6% a year and some in bonds paying 11% per year. She receives a total of \$580 each year from these investments. How much money is invested in stocks and how much money in bonds?

 

[MarkFL]

Re: Algebra word problem

Hello, and welcome to MHB, Mack2002! (Wave)

Let's let $S$ be the amount invested in stocks, and $B$ be the amount invested in bonds. Right away, we know:

\(\displaystyle S+B=6000\tag{1}\)

and:

\(\displaystyle 0.06S+0.11B=580\)

Let's multiply this second equation by 100 to get rid of the decimals:

\(\displaystyle 6S+11B=58000\tag{2}\)

We now have two equations in two unknowns, so we can get an exact solution. Can you now proceed to use the methods for solving simultaneous linear equations you've likely been taught to complete the problem? If not, please show us what you've tried so we can see where you may be going wrong or are having difficulty. :D

 

[Amaterasu]

Re: Algebra word problem

you're right mark
...by the way you spare no free thread for beginners lol
please I know I'm in the wrong section but where can I learn how to insert mathematical symbols while replying thanks in advance

 

[MarkFL]

Re: Algebra word problem

you're right mark
...by the way you spare no free thread for beginners lol

I waited a respectable 56 minutes before replying...(Giggle)

please I know I'm in the wrong section but where can I learn how to insert mathematical symbols while replying thanks in advance

MHB uses $\LaTeX$ powered by MathJax. We also provide tools for easily and quickly constructing and dynamically previewing your $\LaTeX$ code, and then inserting it into your post. In the "Quick $\LaTeX$" element to the right of the editor, you will find most commonly used symbols/commands are categorized via the drop-down menu below the "Symbol/Command Set:" and for each category, you simply click on the symbol or command to insert it into the active element, that is, where your cursor is located.

 

[Fermat1]

Re: Algebra word problem

Not sure how to start this one: Yolanda invests \$6000. Some of the money is invested in stocks paying 6% a year and some in bonds paying 11% per year. She receives a total of \$580 each year from these investments. How much money is invested in stocks and how much money in bonds?

\(\displaystyle x+y=6000\)
\(\displaystyle .06x+.11y=580\)

From first equation, \(\displaystyle x=6000-y\)

Thus,
\(\displaystyle .06(6000-y)+.11y=580\)

\(\displaystyle 360-.06y+.11y=580\)

\(\displaystyle y=4400\)

\(\displaystyle x=6000-y=1600\)

Therefore 1600 in 6% stocks and 4400 in 11% bonds

 

[MarkFL]

Re: Algebra word problem

I would ask that, by our policy, no one provide a complete solution to this problem until the OP has had at least 24 hours to reply to the initial help provided. Thank you. :D

Edit: Now that at least 24 hours has gone by since help was first posted, I have undeleted the post offering a full solution. The trampling of help already given is discouraged in our rules:

Do not explain hints prematurely. When you see someone already helping a member and waiting for the original poster to give feedback, do not give more hints or a full solution. Wait at least 24 hours for the original poster to respond.

Also, we have code in place to remind people who attempt to reply to threads where they are not the OP and they are not the last one to post in the thread and the last post has been made less than 24 hours ago, but we do understand how all of these measures we have taken can be less than 100% effective.

So, when we see that someone has trampled the help provided by another, our usual policy is to soft-delete the trampling post, and then restore it after the requisite 24 hours has passed. We want to get the OP involved in solving the problem, as most of us learn more by doing than by watching. This is why we take this policy so seriously. ;)