document.write( "Question 1209491: Hi
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Algebra.Com's Answer #848927 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "She solved it backwards.  I'll solve it forward, which will probably require\r\n" );
document.write( "a little more work, but it'll be more straight forward.\r\n" );
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document.write( "However, there is a slight flaw in the problem. We are not told that when she\r\n" );
document.write( "saved $45, that this $45 was ALL she had left.  She could have put $45 in her\r\n" );
document.write( "savings account and still had some left over.  But I will assume that she saved\r\n" );
document.write( "ALL that was left.  For otherwise, the problem would not be solvable.\r\n" );
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document.write( "Suppose she had $x at the beginning and each hairpin cost $h.\r\n" );
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document.write( "After spending $90 on a blouse and skirt, she had $(x-90) left.\r\n" );
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document.write( "So then she paid 4h for hair pins and that was equal to 3/8 of $(x-90). So\r\n" );
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document.write( "\"4h=expr%283%2F8%29%28x-90%29\"\r\n" );
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document.write( "Then she had \r\n" );
document.write( "\"%28x-90%29-expr%283%2F8%29%28x-90%29\" left. That's\r\n" );
document.write( "\"%28x-90%29%281-3%2F8%29\"\r\n" );
document.write( "\"%28x-90%29%285%2F8%29\"\r\n" );
document.write( "\"expr%285%2F8%29%28x-90%29\" left\r\n" );
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document.write( "Then she gave 2/5 of that to her mother.  That's \r\n" );
document.write( "\"%282%2F5%29%2Aexpr%285%2F8%29%28x-90%29\" or\r\n" );
document.write( "\"expr%282%2F8%29%28x-90%29\" that she gave to her mother,\r\n" );
document.write( "so she had\r\n" );
document.write( "\"expr%285%2F8%29%28x-90%29\"\"%22%22-%22%22\"\"expr%282%2F8%29%28x-90%29\" or\r\n" );
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document.write( "\"expr%283%2F8%29%28x-90%29\" left\r\n" );
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document.write( "Assuming that she saved ALL the rest,\r\n" );
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document.write( "\"expr%283%2F8%29%28x-90%29=45\"\r\n" );
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document.write( "Multiply both sides by 8\r\n" );
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document.write( "\"3%28x-90%29=360\"\r\n" );
document.write( "\"x-90=120\"\r\n" );
document.write( "\"x=210\" <-- so she had $210 to start with, which was not asked for, but\r\n" );
document.write( "                  could have been. And which you would need to check the problem.\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "\"4h=expr%283%2F8%29%28x-90%29\"\r\n" );
document.write( "\"4h=expr%283%2F8%29%28210-90%29\"\r\n" );
document.write( "\"4h=expr%283%2F8%29\"(120}}}\r\n" );
document.write( "\"4h=45\"\r\n" );
document.write( "\"h=11.25\"\r\n" );
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document.write( "So each hairpin cost $11.25.  <--the answer!\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Rachel had $210 to begin with \r\n" );
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document.write( "Rachel spent $90 on a blouse and shoes. \r\n" );
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document.write( "So she had $120 left.\r\n" );
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document.write( "After that she spent 3/8 of her remaining money on 4 identical hairpins. \r\n" );
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document.write( "Each hairpin cost $11.25 so 4 of them cost $45. So she had $120-$45 = $75 left.\r\n" );
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document.write( "After buying the hairpins, she gave 2/5 of her money she had left to her mother\r\n" );
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document.write( "So she gave 2/5 of $75 or $30 to her mother.\r\n" );
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document.write( "So she had $75 - $30 = $45 left\r\n" );
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document.write( "And since she saved ALL of it, our work is correct.\r\n" );
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document.write( "Edwin
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