Suppose you have $12,000 to invest. If part is invested at 10% and the rest at 15%, how much should be invested at each rate to yield 12% on the total amount invested?

Question

anonymous · Answer

Well...give me a second to solve this...

anonymous · Answer

yay thank you!

anonymous · Answer

lets call the amount invested at 15% $x$ then since the total is 12,000 the amount invested at 10% is $12,000-x$
total return will be 
$$.15x+.10(12,000-x)$$ and you want that to be equal to 12% of 12,000 which is 1440
set 
$$.15x+.10(12,000-x)=1440$$ and solve for $x$

anonymous · Answer

probably easier to multiply by 100 to clear annoying decimals and solve 
$$15x+10(12,000-x)=144,000$$

anonymous · Answer

well the book says it should be 7200 at 10% and 4800 at 15%

anonymous · Answer

so when its 15x youre solving for the15% and if you swtich it to 10x then youre solving for the 10%?