document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214685>Question 214685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange\r<BR>\n" );
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document.write( "Sam invested a total of $10,000, part at 8% and the rest at 3%. How much was invested at 8% if he earned a total of $600 in one year? (Use the formula , Interest = principal * time * rate) \r<BR>\n" );
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document.write( "In an office there was a small cash box. One day Jane took half of the money plus $1 more. Then Mike took half of the remaining money plus $1 more. Rob then took the remaining $6. How many dollars were originally in the box?\r<BR>\n" );
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document.write( "The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162138 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange <BR>\n" );
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document.write( "Equations:<BR>\n" );
document.write( "12r + 7a = 536 cents<BR>\n" );
document.write( "8r  + 5a = 368 cents<BR>\n" );
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document.write( "Get rid of the \"a's\":<BR>\n" );
document.write( "Multiply 1st Eq. by 5 and 2nd Eq. by 7 to get:<BR>\n" );
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document.write( "60r + 35a = 5*536<BR>\n" );
document.write( "56r + 35a = 7*368<BR>\n" );
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document.write( "Subtract the 2nd from the 1st and solve for \"r\":<BR>\n" );
document.write( "4r = 104<BR>\n" );
document.write( "r = 26 cents (cost of one orange)<BR>\n" );
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document.write( "Sam invested a total of $10,000, part at 8% and the rest at 3%. How much was invested at 8% if he earned a total of $600 in one year? (Use the formula , Interest = principal * time * rate) <BR>\n" );
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document.write( "Interest + interest = interest<BR>\n" );
document.write( "0.08x + 0.03(10000-x) = 600<BR>\n" );
document.write( "Multiply thru by 100 to get:<BR>\n" );
document.write( "8x + 30000 - 3x = 60000<BR>\n" );
document.write( "5x = 30000<BR>\n" );
document.write( "x = 6000 (amt invested at 8%)<BR>\n" );
document.write( "4000 (amt invested at 3%)<BR>\n" );
document.write( "==============================\r<BR>\n" );
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document.write( "In an office there was a small cash box. One day Jane took half of the money plus $1 more. Then Mike took half of the remaining money plus $1 more. Rob then took the remaining $6. How many dollars were originally in the box? <BR>\n" );
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document.write( "Start : x<BR>\n" );
document.write( "After Jane: x -(1/2)x-1 = (1/2)x -1<BR>\n" );
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document.write( "After Mike: [(1/2)x-1] - [(1/2)x-1]/2 -1 = (1/2)[(1/2)x-1]-1<BR>\n" );
document.write( "= (1/4)x - (3/2)\r<BR>\n" );
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document.write( "-----------------------------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "(1/4)x - (3/2) = 6<BR>\n" );
document.write( "(1/4)x = 7.5<BR>\n" );
document.write( "x = 30<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "30 -(15+1) = 14<BR>\n" );
document.write( "14-(7+1) = 6<BR>\n" );
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document.write( "OK<BR>\n" );
document.write( "Original amount = $30<BR>\n" );
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document.write( "The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number?<BR>\n" );
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document.write( "Equations:<BR>\n" );
document.write( "a + b = 2a-8<BR>\n" );
document.write( "a - b = 2b-4<BR>\n" );
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document.write( "Rearrange:<BR>\n" );
document.write( "a = b + 8<BR>\n" );
document.write( "a = 3b-4<BR>\n" );
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document.write( "Substitute to get:<BR>\n" );
document.write( "b+8 = 3b-4<BR>\n" );
document.write( "2b = 12<BR>\n" );
document.write( "b = 6<BR>\n" );
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document.write( "Substitute into a = b+8 to get:<BR>\n" );
document.write( "a = 14<BR>\n" );
document.write( "================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );