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Math Help - System of equations-please help!!

  1. #1
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    System of equations-please help!!

    Mr. Johnson has invested $30,000 part @ 4% and part @ 7%. His annual interest from the two investments is $1500. How much is invested @ each rate?

    So far I have the first equation, I think, but I can't figure out how to write the second part. This is what I've set up already:

    .4x + .7y=30000

    In order to solve for x and y, I still need to figure out the second equation. Any ideas?
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  2. #2
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    Quote Originally Posted by acharles View Post
    Mr. Johnson has invested $30,000 part @ 4% and part @ 7%. His annual interest from the two investments is $1500. How much is invested @ each rate?

    So far I have the first equation, I think, but I can't figure out how to write the second part. This is what I've set up already:

    .4x + .7y=30000

    In order to solve for x and y, I still need to figure out the second equation. Any ideas?
    Let x denote the part of the $30.000 which is invested at 4 %;

    then ($30.000 - x) are invested at 7 %.

    Therefore:

    4%*x + 7%*($30.000 - x) = $1.500

    "Translate" the percents into fractions and you'll get:

    \frac4{100} \cdot x + \frac7{100} \cdot (\$30.000 - x) = \$1.500

    Solve for x. For confirmation only: I've got x = $20.000
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    Re:

    So do I still use the first equation or was that wrong? Don't I need an equation with y too?
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  4. #4
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    Quote Originally Posted by acharles View Post
    So do I still use the first equation or was that wrong? Don't I need an equation with y too?
    1. You don't need a second variable, if you calculate the value of the second part as ($30.000 - x).

    2. You used the wrong values: 0.4 = 40%. If you aren't sure that you have done the transformation percent --> fraction correctly than use fractions with the denominator 100. So 4% = 4/100.
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    Still confused

    I'm not sure how to solve for x when I don't have a y variable to plug into the equation. I can do that?
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  6. #6
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    Quote Originally Posted by acharles View Post
    Mr. Johnson has invested $30,000 part @ 4% and part @ 7%. His annual interest from the two investments is $1500. How much is invested @ each rate?

    So far I have the first equation, I think, but I can't figure out how to write the second part. This is what I've set up already:

    .4x + .7y=30000

    In order to solve for x and y, I still need to figure out the second equation. Any ideas?
    OK, once again:

    Let x denote the part of the $30.000 which is invested at 4 %;

    then y are invested at 7 %.

    Now you know:
    <br />
\left| \begin{array}{lcr}x+y&=&30000 \\ <br />
0.04\cdot x+0.07\cdot y &=& 1500 \end{array}\right.

    Solve the first equation for y = 30000-x and plug this term into the second equation:

    0.04\cdot x+0.07\cdot (30000-x)= 1500

    Expand the bracket, collect like terms, solve for x.

    Resubstitute the value of x into the equation calculating y.

    You already know the results.
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