document.write( "Question 1202333: David spent $75 of his money on some t-shirts. He spent 1/4 of the remaining money on some batteries. Given that he was left with 1/3 of his original sum of money left, how much money did David have at first? \n" ); document.write( "
Algebra.Com's Answer #837073 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Answer: $135\r
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\n" ); document.write( "\n" ); document.write( "Work Shown:\r
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\n" ); document.write( "\n" ); document.write( "x = starting amount of money
\n" ); document.write( "x-75 = amount left after buying the shirts
\n" ); document.write( "(1/4)*(x-75) = amount spent on batteries
\n" ); document.write( "(3/4)(x-75) = amount leftover after buying the batteries\r
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\n" ); document.write( "\n" ); document.write( "Note that 1/4 + 3/4 = 1 = 100% of his money\r
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\n" ); document.write( "\n" ); document.write( "That last expression is set equal to (1/3)x because David is left with 1/3 of his original money.\r
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\n" ); document.write( "\n" ); document.write( "(3/4)(x-75) = (1/3)x
\n" ); document.write( "12*(3/4)(x-75) = 12*(1/3)x
\n" ); document.write( "9(x-75) = 4x
\n" ); document.write( "9x-675 = 4x
\n" ); document.write( "9x-4x = 675
\n" ); document.write( "5x = 675
\n" ); document.write( "x = 675/5
\n" ); document.write( "x = 135
\n" ); document.write( "David started off with $135\r
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "Start = 135
\n" ); document.write( "Buy the shirts: 135-75 = 60 dollars left
\n" ); document.write( "(1/4)*60 = 15 dollars spent on batteries
\n" ); document.write( "60-15 = 45 dollars at the end
\n" ); document.write( "45/135 = 1/3 of what he started with
\n" ); document.write( "The answer is confirmed.
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