SOLUTION: Could you guide me about the following problem?Tanks.. N.has invested a total of $8000, some at 4% and the rest at 7%. If the 4% invenstment yields $155 more than the 7% invenstme

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Could you guide me about the following problem?Tanks.. N.has invested a total of $8000, some at 4% and the rest at 7%. If the 4% invenstment yields $155 more than the 7% invenstme      Log On


   

Question 202008: Could you guide me about the following problem?Tanks..
N.has invested a total of $8000, some at 4% and the rest at 7%. If the 4% invenstment yields $155 more than the 7% invenstment, how much was invested at 4%?
I've written: 8000=2x+155 . Is it correct or I must use of either 4% and 7%?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

x = amount invested at 4%
y = amount invested at 7%



"N.has invested a total of $8000" means that x%2By=8000. Solving for "y" gets us y=-x%2B8000


Since "the 4% investment yields $155 more than the 7% investment", we know that 0.04x=0.07y%2B155


Now multiply EVERY term by 100 to get 4x=7y%2B15500


4x=7%28-x%2B8000%29%2B15500 Now plug in y=-x%2B8000


4x=-7x%2B56000%2B15500 Distribute.


4x=-7x%2B71500 Combine like terms on the right side.


4x%2B7x=71500 Add 7x to both sides.


11x=71500 Combine like terms on the left side.


x=%2871500%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=6500 Reduce.


y=-x%2B8000 Go back to the previously isolated equation


y=-6500%2B8000 Plug in x=6500


y=1500 Add


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Answer:


So the solutions are x=6500 and y=1500


This means that $6,500 was invested at 4% while $1,500 was invested at 7%