Question 189605
Let x=amount invested at 8% and y=amount invested at 11%



"A man invest $7000 for one year" translates to {{{x+y=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+0.11y=764}}}



Multiply every term by 100 to get {{{8x+11y=76400}}}



So we have the system



{{{system(x+y=7000,8x+11y=76400)}}}



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+y=7000}}} Start with the first equation



{{{y=7000-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+7000}}} Rearrange the equation


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


Since {{{y=-x+7000}}}, we can now replace each {{{y}}} in the second equation with {{{-x+7000}}} to solve for {{{x}}}




{{{8x+11highlight((-x+7000))=76400}}} Plug in {{{y=-x+7000}}} into the second equation. In other words, replace each {{{y}}} with {{{-x+7000}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{8x+(11)(-1)x+(11)(7000)=76400}}} Distribute {{{11}}} to {{{-x+7000}}}



{{{8x-11x+77000=76400}}} Multiply



{{{-3x+77000=76400}}} Combine like terms on the left side



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



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



{{{x=(-600)/(-3)}}} 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+7000}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+7000}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(200)+7000}}} Plug in {{{x=200}}}



{{{y=-200+7000}}} 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%