document.write( "Question 1049016: Last year, Tony had $20,000 to invest. He invested some of it in an account that paid 5% simple interest per year, and he invested the rest in an account that paid 6% simple interest per year. After one year, he received a total of $1170 in interest. How much did he invest in each account? \n" ); document.write( "

Algebra.Com's Answer #664578 by advanced_Learner(501) $\"\"$ $\"About$

You can put this solution on YOUR website!
let $\"a\"$ stand for amount invested at $\"5%25\"$ then $\"2000-a\"$ paid $\"6%25\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"interest\"$ + $\"interest\"$ = $\"interest\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"5%25\"$ $\"a\"$ + $\"6%25\"$ ( $\"20000-a\"$ )= $\"1170\"$
\n" ); document.write( " $\"0.05\"$ $\"a\"$ + $\"0.06\"$ ( $\"20000-a\"$ )= $\"1170\"$
\n" ); document.write( " $\"5\"$ $\"a\"$ + $\"6\"$ ( $\"20000-a\"$ )= $\"117000\"$
\n" ); document.write( " $\"5\"$ $\"a\"$ +( $\"120000-6a\"$ )= $\"117000\"$
\n" ); document.write( " $\"12000-a\"$ = $\"117000\"$
\n" ); document.write( " $\"-a\"$ = $\"117000\"$ - $\"120000\"$
\n" ); document.write( " $\"-a\"$ = $\"117000\"$ - $\"120000\"$
\n" ); document.write( " $\"-a\"$ = $\"-3000\"$
\n" ); document.write( " $\"a\"$ = $\"3000\"$ \r
\n" ); document.write( "\n" ); document.write( "you solve for $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3000\"$ at $\"5%25\"$ and $\"20000-3000\"$
\n" ); document.write( "which means $\"17000\"$ at $\"6%25\"$ \r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: a=3000.
Graphical form: Equation $\"5a%2B120000-6a=117000\"$ was fully solved.
Text form: 5a+120000-6a=117000 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+5a%2B120000-6a=117000+%29\"$
For tutors: simplify_cartoon( 5a+120000-6a=117000 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"5%2Aa%2Bhighlight_red%28+120000+%29-6%2Aa=117000\"$ .
Moved $\"120000\"$ to the right of expression
It becomes $\"5%2Aa-6%2Aa%2Bhighlight_green%28+120000+%29=117000\"$ .
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Look at $\"highlight_red%28+5%2Aa+%29-highlight_red%28+6%2Aa+%29%2B120000=117000\"$ .
Eliminated similar terms $\"highlight_red%28+5%2Aa+%29\"$ , $\"highlight_red%28+-6%2Aa+%29\"$ replacing them with $\"highlight_green%28+%285-6%29%2Aa+%29\"$
It becomes $\"highlight_green%28+%285-6%29%2Aa+%29%2B120000=117000\"$ .
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Look at $\"%28highlight_red%28+5+%29-highlight_red%28+6+%29%29%2Aa%2B120000=117000\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-1+%29%29%2Aa%2B120000=117000\"$ .
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Look at $\"%28highlight_red%28+-1+%29%29%2Aa%2B120000=117000\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"%28-highlight_green%28+1+%29%29%2Aa%2B120000=117000\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+1+%29%29%2Aa+%29%2B120000=117000\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$
It becomes $\"-highlight_green%28+1+%29%2Aa%2B120000=117000\"$ .
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Look at $\"-highlight_red%28+1+%29%2Aa%2B120000=117000\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"-a%2B120000=117000\"$ .
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Look at $\"-a%2B120000=highlight_red%28+117000+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-117000+%29\"$
It becomes $\"-a%2B120000-highlight_green%28+117000+%29=0\"$ .
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Look at $\"-a%2Bhighlight_red%28+120000+%29-highlight_red%28+117000+%29=0\"$ .
Added fractions or integers together
It becomes $\"-a%2Bhighlight_green%28+3000+%29=0\"$ .
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Look at $\"highlight_red%28+-a%2B3000+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-a%2B3000=0+%29\"$ equivalent to -a+3000 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: a=3000.

Universal Simplifier and Solver

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Done!

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