document.write( "Question 41616: Lane invested $10,000, part at 15% and part at 14%.
\n" ); document.write( "If the total interest at the end of the year is $1,430, how much did she invest at 15%?
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Algebra.Com's Answer #26902 by tutorcecilia(2152)\"\" \"About 
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This is a type of mixture problem.
\n" ); document.write( "The formula to remember is:
\n" ); document.write( "(rate of A)(amount of A) + (rate of B)(amount of B) = Total Value
\n" ); document.write( "Rate A = 15% = .15
\n" ); document.write( "Amount A = \"how much\" = x
\n" ); document.write( "Rate B = 14% = .14
\n" ); document.write( "Total Value = \"the total amount of interest\" = $1430 (this wording is confusing because this is really the \"Total Value of interest of $10,000)
\n" ); document.write( ".
\n" ); document.write( "Total Amount invested = $10,000 =(Amount of A + Amount B)
\n" ); document.write( "So, 10,000 - A = B
\n" ); document.write( "or 10,000 - B = A
\n" ); document.write( ".
\n" ); document.write( "Putting it all together:
\n" ); document.write( "(.15)(x) + (.14)(10,000 - x) = 1430
\n" ); document.write( "Simplifying:
\n" ); document.write( ".15x + (1400 -.14x) = 1430
\n" ); document.write( ".15x + 1400 - .14x = 1430
\n" ); document.write( ".01x + 1400 - 1400 = 1430 - 1400
\n" ); document.write( ".01x = .30
\n" ); document.write( ".01x/.01 = 30/.01
\n" ); document.write( "x = 3000
\n" ); document.write( ".
\n" ); document.write( "Plugging x=3000 back into the original equation:
\n" ); document.write( "(.15)(x) + (.14)(10,000 - x) = 1430
\n" ); document.write( "(.15)(3000) + (.14)(10,000 - 3000) = 1430
\n" ); document.write( "450 + 980 = 1430
\n" ); document.write( "1430 = 1430\r
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