SOLUTION: Dave Horn invested half of his money at 5%, one-tird of his money at4%, and the rest at 3.5%. If his total annual investment incomw is $530, how much had he invested?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Dave Horn invested half of his money at 5%, one-tird of his money at4%, and the rest at 3.5%. If his total annual investment incomw is $530, how much had he invested?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 419077: Dave Horn invested half of his money at 5%, one-tird of his money at4%, and the rest at 3.5%. If his total annual investment incomw is $530, how much had he invested?
Found 3 solutions by mananth, ikleyn, josgarithmetic:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
let total money invested be x
percent
5 0.33
4 0.50x
3.5 0.17x

Total income = 530
1.67 x + 2 x +
4.25 x 53000
/ 4.25
x = 12470.59
Interest
5.00%---------- 4156.86
4.00%---------- 6235.29
3.50%---------- 2078.43




Answer by ikleyn(53427) About Me  (Show Source):
You can put this solution on YOUR website!
.
Dave Horn invested half of his money at 5%, one-tird of his money at4%, and the rest at 3.5%.
If his total annual investment income is $530, how much had he invested?
~~~~~~~~~~~~~~~~~~~~~~~~


        @mananth incorrectly interpreted the problem and incorrectly treated it.
        Therefore, his solution and his answer both are incorrect.
        I came to bring a correct solution. 


percent    part   
  5        1/2
  4        1/3
  3.5      the rest = 1 - 1/2 - 1/3 = 1 - 5/6 = 1/6


Let x be the total investment.

Write an equation for the total interest

    0.05%2A%28x%2F2%29 + 0.04%2A%28x%2F3%29 + 0.035%2A%28x%2F6%29 = 530 dollars.


It is your setup equation.  Now you should find the unknown x from it.
For it, first multiply this equation by 6 to rid the denominators.  You will get

    0.05*(3x) + 0.04*(2x) + 0.035x = 6*530,

    0.15x + 0.08x + 0.035x = 3180.

            0.265x         = 3180,

                 x         = 3180/0.265 = 12000.


ANSWER.  $6000 was invested at 5%;  $4000 was invested at 4%,  and  $2000 was invested at 3.5%.


CHECK.  0.05*6000 + 0.04*4000 + 0.035*2000 = 530  dollars.   ! correct !

Solved correctly.



Answer by josgarithmetic(39702) About Me  (Show Source):
You can put this solution on YOUR website!
RATE%              INVEST              INCOME
   5                 p/2                0.05(p/2)
   4                 p/3                0.04(p/3)
   3.5             p-p/2-p/3=p/6        0.035(p/6)
TOTAL                                    530

%280.05%2F2%2B0.04%2F3%2B0.035%29p=530
l.c.d. is 12
12p%280.05%2F2%2B0.04%2F3%2B0.035%2F6%29=530%2A12
.
.
%280.3%2B0.16%2B0.07%29p=6360
0.53p=6360
highlight%28p=12000%29 the original amount invested among the three accounts.
6000 at 5%
4000 at 4%
2000 at 3.5%