Question 202008
Let 


x = amount invested at 4%

y = amount invested at 7%




"N.has invested a total of $8000" means that {{{x+y=8000}}}. Solving for "y" gets us {{{y=-x+8000}}}



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



Now multiply EVERY term by 100 to get {{{4x=7y+15500}}}



{{{4x=7(-x+8000)+15500}}} Now plug in {{{y=-x+8000}}}



{{{4x=-7x+56000+15500}}} Distribute.



{{{4x=-7x+71500}}} Combine like terms on the right side.



{{{4x+7x=71500}}} Add {{{7x}}} to both sides.



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



{{{x=(71500)/(11)}}} Divide both sides by {{{11}}} to isolate {{{x}}}.



{{{x=6500}}} Reduce.



{{{y=-x+8000}}} Go back to the previously isolated equation



{{{y=-6500+8000}}} 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%