Question 1138527: Mr. Lopez has two sums of money earning interests, one at 3%, the other at 4%. His annual income from the two investment is 410 pesos. If he could get 4% on all of his money this income would be 480 pesos. How much did he invest at each rate?
Answer by ikleyn(52814)   (Show Source):
You can put this solution on YOUR website! .
If he could get 4% on ALL of his money, his income would be 480 pesos.
It means that the total of two investments is  = 12000 pesos.
Let x = amount at 3%, in pesos.
Then the amount at 4% is the rest (12000-x) pesos.
The interest from the 3% amount is 0.03*x pesos.
The interest from the 4% amount is 0.04*(12000-x) pesos.
Your equation is
interest + interest = total interest, or
0.03*x + 0.04*(12000-x) = 410 pesos.
From the equation, express x and calculate the answer
x =  = 7000.
Answer. The amount at 3% is $7000; the rest $12000-$7000 = $5000 is the amount at 4%.
Check. 0.03*7000 + 0.04*5000 = 410 pesos. ! Correct !
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It is a typical and standard problem on investment.
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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