SOLUTION: Please help me solve this equation: Pat invested a total of $3,000. Part of the money yields 10 percent interest per year, and the rest

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Let x=amount invested at 10% and y=amount invested at 8%


"Pat invested a total of $3,000" translates to


"Part of the money yields 10 percent interest
per year, and the rest yields 8 percent interest per year. If the total yearly
interest from this investment is $256" translates to


Multiply both sides by 100 to get



So we have the system of equations:




Let's solve by substitution


Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

Start with the first equation


Subtract from both sides


Rearrange the equation



---------------------

Since , we can now replace each in the second equation with to solve for



Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute to


Multiply


Combine like terms on the left side


Subtract 24000 from both sides


Combine like terms on the right side


Divide both sides by 2 to isolate x



Divide





-----------------First Answer------------------------------


So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is:









-----------------Summary------------------------------

So our answers are:

and


So this means that Pat invested $800 at 10% and $2,200 at 8%

You can put this solution on YOUR website!
let x and y be the amounts invested at 10% and 8%
:
x+y=3000........eq 1
.1x+.08y=256....eq 2
:
rewrite eq 1 to x=3000-y and plug that value into eq2
:
.1(3000-y)+.08y=256
:
300-.1y+.08y=256
:
-.02y=-44
:
$amount invested at 8%
:
$amount invested at 10%