Thread: 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?

Originally Posted by acharles

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:

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

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

So do I still use the first equation or was that wrong? Don't I need an equation with y too?

Originally Posted by acharles

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.

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?

Originally Posted by acharles

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:
$\displaystyle
\left| \begin{array}{lcr}x+y&=&30000 \\
0.04\cdot x+0.07\cdot y &=& 1500 \end{array}\right.$

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

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

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

Resubstitute the value of x into the equation calculating y.

You already know the results.