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Question 1122104: Ms Jami plans to invest $3,800 in two accounts for one year. The first account earns a yearly interest of 3.5%.The second account earns a yearly interest of 6%.How much money does Ms Jami need to invest in order to earn $188 in interest from both accounts
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52933)   (Show Source):
You can put this solution on YOUR website! .
Let x = amount at 3.5%.
Then the amount at 6% is (3800-x).
The interest from the 3.5% amount is 0.035*x dollars.
The interest from the 6% amount is 0.06*x dollars.
Your equation is
interest + interest = total interest, or
0.035*x + 0.06*(3800-x) = 188 dollars.
x =  = 1600.
Answer. The amount at 3.5% is $1600; the rest $3800-$1600 = $2200 is the amount at 6%.
Check. 0.035*1600 + 0.06*2200 = 188 dollars. ! 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.
Answer by greenestamps(13216)  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the standard algebraic solution method shown by the other tutor. If you understand this method, it will get you to the answer much faster and with less work than the algebraic method -- especially if you are good with some mental arithmetic.
To show you how fast the solution process can be, I'll first just show you the calculations that are required; then I will explain the process.
(1) 3800*.035 = 133; 3800*.06 = 228
(2) 228-188 = 40; 188-133 = 55
(3) 40:55 = 8:11
(4) (8/19)3800 = 8*200 = 1600; (11/19)3800 = 11*200 = 2200
(5) Answer: $2200 at 6%; $1600 at 3.5%.
In the first three steps, we determine the ratio in which the money needs to be split by comparing the actual amount of interest to the amounts of interest if all the money had been invested at each of the two rates.
Step 1: determine the amounts of interest if all the money were invested at each of the rates.
Step 2: find how far the actual interest amount is from each of the amounts in step 1.
step 3: express the distances that the actual amount of interest is from the two amounts in step 1 as a ratio.
That ratio ratio is the ratio in which the money needs to be split between the two accounts. The actual interest is closer to $228 than to $133, so the larger portion needs to be invested at the higher rate.
Step 4: convert the ratio into two fractions that are the fractions of the total that needs to be invested at each rate; multiply the total amount by each of those two fractions to find the amounts that need to be invested at each rate.
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