SOLUTION: James has a certain amount of money invested at 5% annual interest and $500 more than twice that amount invested in bonds yielding 7%. His total annual income from interest is $187

Question 1152475: James has a certain amount of money invested at 5% annual interest and $500 more than twice that amount invested in bonds yielding 7%. His total annual income from interest is $187. How much does he have invested at each rate?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x equals the amount of money he has invested at 5%.
2x + 500 equals the amount of money he has invested at 7%.
.05x + .07 * (2x + 500) = 187
simplify to get:
.05x + .14x + 35 = 187
combine like terms and subtract 35 from both sides of the equation to get:
.19x = 152
solve for x to get:
x = 800
2x + 500 = 2100
.05 * 800 + .07 * 2100 = 187
this confirms the value for x is good.
your solution is:
he has 800 invested at 5% and 2100 invested at 7%.

Answer by ikleyn(52906)   (Show Source): You can put this solution on YOUR website!
.

Let x be the amount invested at 5%. Then the amount invested at 7% is (2x+500) dollars. The partial interests are 0.05x dollars and 0.07*(2x+500) dollars. The equation for the total interest is 0.05x + 0.07*(2x+500) = 187 dollars. From the equation x = = 800. ANSWER. $800 were invested at 5%, and 2*800+500 = 2100 dollars were invested at 7%. CHECK. 0.05*800 + 0.07*2100 = 187 dollars. ! Precisely correct !

Solved.

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It is a standard and typical problem on investments.

If you need more details, or if you want to see other similar problems solved by different methods, 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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