document.write( "Question 1049657: The annual interest on an $8000 investment exceeds the interest earned on a $2000 investment by $392. The $8000 is invested at a 0.4% higher rate of interest than the $2000. What is the interest rate of each investment? \n" ); document.write( "

Algebra.Com's Answer #665238 by advanced_Learner(501) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28x%2B0.004%29%248000\"$ = $\"%28x%29%242000%2B392\"$
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: x=0.06.
Graphical form: Equation $\"%28x%2B0.004%29%2A8000-2000%2Ax=392\"$ was fully solved.
Text form: (x+0.004)*8000-2000*x=392 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+%28x%2B0.004%29%2A8000-2000%2Ax=392+%29\"$
For tutors: simplify_cartoon( (x+0.004)*8000-2000*x=392 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"%28x%2B0.004%29%2A8000-2000%2Ax=highlight_red%28+392+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-392+%29\"$
It becomes $\"%28x%2B0.004%29%2A8000-2000%2Ax-highlight_green%28+392+%29=0\"$ .
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Look at $\"highlight_red%28+%28x%2B0.004%29%2A8000+%29-2000%2Ax-392=0\"$ .
Expanded term $\"8000\"$ by using associative property on $\"%28x%2B0.004%29\"$
It becomes $\"highlight_green%28+8000%2Ax+%29%2Bhighlight_green%28+8000%2A0.004+%29-2000%2Ax-392=0\"$ .
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Look at $\"8000%2Ax%2Bhighlight_red%28+8000%2A0.004+%29-2000%2Ax-highlight_red%28+392+%29=0\"$ .
Replace constants in expression: $\"highlight_red%28+8000%2A0.004+%29\"$ , $\"highlight_red%28+-392+%29\"$ with $\"highlight_green%28+-360+%29\"$
It becomes $\"highlight_green%28+-360+%29%2B8000%2Ax-2000%2Ax=0\"$ .
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Look at $\"highlight_red%28+-360+%29%2B8000%2Ax-2000%2Ax=0\"$ .
Moved $\"-360\"$ to the right of expression
It becomes $\"8000%2Ax-2000%2Ax%2Bhighlight_green%28+-360+%29=0\"$ .
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Look at $\"8000%2Ax-2000%2Ax%2Bhighlight_red%28+-360+%29=0\"$ .
Removed extra sign in front of $\"-360\"$
It becomes $\"8000%2Ax-2000%2Ax-highlight_green%28+360+%29=0\"$ .
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Look at $\"highlight_red%28+8000%2Ax+%29-highlight_red%28+2000%2Ax+%29-360=0\"$ .
Eliminated similar terms $\"highlight_red%28+8000%2Ax+%29\"$ , $\"highlight_red%28+-2000%2Ax+%29\"$ replacing them with $\"highlight_green%28+%288000-2000%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%288000-2000%29%2Ax+%29-360=0\"$ .
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Look at $\"%28highlight_red%28+8000+%29-highlight_red%28+2000+%29%29%2Ax-360=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+6000+%29%29%2Ax-360=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+6000+%29%29%2Ax+%29-360=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+6000+%29\"$
It becomes $\"highlight_green%28+6000+%29%2Ax-360=0\"$ .
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Look at $\"highlight_red%28+6000%2Ax-360+%29=0\"$ .
Solved linear equation $\"highlight_red%28+6000%2Ax-360=0+%29\"$ equivalent to 6000*x-360 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
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Universal Simplifier and Solver

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Done!

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