document.write( "Question 288233: Ben invested some money at 8% simple interest and $100 more than this amount at 7%. His total annual interest was $82. How much did he invest at each rate? \n" ); document.write( "

Algebra.Com's Answer #208903 by jaydducote(11) $\"\"$ $\"About$

You can put this solution on YOUR website!
So the unknown is how much he invested at 8%, so that will be the variable, x.
\n" ); document.write( "We know he invested $100 more at 7%, so he invested x+100 at 7%.
\n" ); document.write( "Simple interest is not compounded, so we know that since it says \"annual\" interest, the time period is one year, so he will make exactly 7% and 8% of the amounts. Therefor, we can use the following formula:
\n" ); document.write( ".08x+.07(x+100)=82
\n" ); document.write( "Make sure you convert 8% to .08 and 7% to .07. Percent means \"per 100\", so 7% is 7/100, or .07.\r
\n" ); document.write( "\n" ); document.write( "distribute the .07 to get:
\n" ); document.write( ".08x+.07x+7=82
\n" ); document.write( "combine like terms
\n" ); document.write( ".15x+7=82
\n" ); document.write( "subtract 7 from both sides
\n" ); document.write( ".15x=75
\n" ); document.write( "divide both sides by .15
\n" ); document.write( "x=500
\n" ); document.write( "this means that 500 was invested at 8% and (x+100 so 500+100) 600 was invested at 7%. \n" ); document.write( "

\n" );