.
Let x = amount invested at 5.5% annual.
Then the amount invested at 6% annual is (x+8000) dollars, according to the condition.
The major equation is
interest + interest = total interest, or
0.055*x + 0.06*(x+8000) = 1630
0.055x + 0.06x + 0.06*8000 = 1630
0.115x = 1630 - 0.06*8000 = 1150 ====> x = = 10000.
Answer. $10000 was invested at 5.5% and 18000 was invested at 6%.
Check. 0.055*10000 + 0.06*18000 = 1630 dollars. ! Correct !
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To see many other similar solved problems on investment, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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Be aware !: The solution by @mananth is T O T A L L Y W R O N G and I R R E L E V A N T.
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Hello, @amanth !
It is just some days in a row you make one fatal error after another in yours so called "solutions".
I see that you have serious problems with reading and understanding simple algebra problems.
Such a miserable level is not allowed for a tutor.
I am not happy to spend my efforts and my reputation in this forum to clean garbage after you . . .
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Dear tutor @grenestamps,
When I worked at Bectel Corporation (San Francisco) fifteen years ago, I attended the lessons on English as a Second language
(just having the basic knowledge - just to improve it).
Our teacher, native American speaker, said us once: "Do not search/(do not look) for a logic in using prepositions in English.
There is no logic there. There are rules of precedence only . . . "
We all were laughing then. After years, I undestood beter and better his words . . .
In distinct of many other languages (mostly of a Roman origin), English is built on standard constructions and standard combinations of words.
At least, it is true for the "everyday English", for "plain English" and even/(and also) for the "textbook English" in textbooks up to high school.
Each such standard combination of words is a "paradigm".
Saying "and $8000 more at 6%" is a standard paradigm replacing "and $8000 more than SOMETHING at 6%".
It is the same as to call it (= as you call it) "usual interpretation".
Interpretation of this combination as "and additional $8000 at 6%" is totally different paradigm, and these two different paradigms are never missed in textbooks.
Therefore, when I say that @mananth incorrectly interpret that standard paradigm, I mean EXACTLY this fact that he DOES NOT know the standard paradigm.
It is exactly what I am argue about, regarding his solution.
Your notice recalled me the words of my English teacher. Formally you are right. Bad for English, although, that two so close and so different paradigms may coexist
as almost undistinguishable.
Still, I think that nobody in healthy mind will use this alternative combination of words to describe the situation. // Or to interpret the situation in this way.
Although, again, the users and visitors of this forum are so different, that everything may happen . . .
At this point I'd like to close this theme.
My apologies to the student for this discussion, which does not relate to him . . .