SOLUTION: I have used the solvers presented but I am unable to get the correct answer for the following: A man invest $7000 for one year. He invested part of it at 8% and the rest at 12%.

Algebra ->  Finance -> SOLUTION: I have used the solvers presented but I am unable to get the correct answer for the following: A man invest $7000 for one year. He invested part of it at 8% and the rest at 12%.       Log On


   

Question 189605: I have used the solvers presented but I am unable to get the correct answer for the following: A man invest $7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest. How much did he invest at each rate? This is a quiz question.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount invested at 8% and y=amount invested at 11%


"A man invest $7000 for one year" translates to x%2By=7000


"He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest" translates to 0.08x%2B0.11y=764


Multiply every term by 100 to get 8x%2B11y=76400


So we have the system


system%28x%2By=7000%2C8x%2B11y=76400%29


Let's solve this system 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

x%2By=7000 Start with the first equation


y=7000-x Subtract x from both sides


y=-x%2B7000 Rearrange the equation

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

Since y=-x%2B7000, we can now replace each y in the second equation with -x%2B7000 to solve for x



8x%2B11highlight%28%28-x%2B7000%29%29=76400 Plug in y=-x%2B7000 into the second equation. In other words, replace each y with -x%2B7000. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



8x%2B%2811%29%28-1%29x%2B%2811%29%287000%29=76400 Distribute 11 to -x%2B7000


8x-11x%2B77000=76400 Multiply


-3x%2B77000=76400 Combine like terms on the left side


-3x=76400-77000Subtract 77000 from both sides


-3x=-600 Combine like terms on the right side


x=%28-600%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=200 Divide





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


So the first part of our answer is: x=200









Since we know that x=200 we can plug it into the equation y=-x%2B7000 (remember we previously solved for y in the first equation).



y=-x%2B7000 Start with the equation where y was previously isolated.


y=-%28200%29%2B7000 Plug in x=200


y=-200%2B7000 Multiply


y=6800 Combine like terms



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


So the second part of our answer is: y=6800









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

So our answers are:

x=200 and y=6800


This means that $200 was invested at 8% while $6,800 was invested at 11%