document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62036>Question 62036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1) A history instructor is undecided on the amount of weight to give each type of question on his test, but knows that because of time restrictions, he can only ask a certain number of each type.  If multiple-choice questions are worth 7 points each and the true-false questions worth 2 points each, the test will be worth a total of 185 points.  If the multiple-choice and true-false questions are worth 4 points each, the test will be worth a total of 200 points.  Find the number of multiple-choice questions and the number of true-false questions that he will have on the test.\r<BR>\n" );
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document.write( "(2) My friend and I went out to lunch last week, but we did not pay attention to the cost of each item we ordered until we compared receipts.  I had one soft drink and one taco.  My bill showed a tax of 15 cents and a total of $2.25.  My friend had two soft drinks and three tacos.  His bill showed a tax of 36 cents and a ottal of $5.51.  How much was each item (before tax)?\r<BR>\n" );
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document.write( "(3) Given below are two equivalent systems of equations. Find the value of A and B.<BR>\n" );
document.write( "x + 2y = 2<BR>\n" );
document.write( "5x - 3y = -29<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Ax + 5y = -9<BR>\n" );
document.write( "x + By = 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42925 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A history instructor is undecided on the amount of weight to give each type of question on his test, but knows that because of time restrictions, he can only ask a certain number of each type. If multiple-choice questions are worth 7 points each and the true-false questions worth 2 points each, the test will be worth a total of 185 points. If the multiple-choice and true-false questions are worth 4 points each, the test will be worth a total of 200 points. Find the number of multiple-choice questions and the number of true-false questions that he will have on the test<BR>\n" );
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document.write( "Let x = no. of mult choice; y = no. of true/false<BR>\n" );
document.write( "1st case:<BR>\n" );
document.write( "7x + 2y = 185<BR>\n" );
document.write( "2nd case:<BR>\n" );
document.write( "4x + 4y = 200<BR>\n" );
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document.write( "Mult the 2nd equation by .5 and subtract it from the 1st equation<BR>\n" );
document.write( "7x + 2y = 185<BR>\n" );
document.write( "2x + 2y = 100<BR>\n" );
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document.write( "5x + 0y = 85<BR>\n" );
document.write( "x = 85/5<BR>\n" );
document.write( "x = 17 mult ch questions<BR>\n" );
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document.write( "Find the true/false using the 1st equation<BR>\n" );
document.write( "7(17) + 2y = 185<BR>\n" );
document.write( "119 + 2y = 185<BR>\n" );
document.write( "2y = 185 - 119<BR>\n" );
document.write( "2y = 66<BR>\n" );
document.write( "y = 33 true/false questions<BR>\n" );
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document.write( "Check solutions in the 2nd equation:<BR>\n" );
document.write( "4(17) + 4(33) = 200<BR>\n" );
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document.write( "(2) My friend and I went out to lunch last week, but we did not pay attention to the cost of each item we ordered until we compared receipts. I had one soft drink and one taco. My bill showed a tax of 15 cents and a total of $2.25. My friend had two soft drinks and three tacos. His bill showed a tax of 36 cents and a total of $5.51. How much was each item (before tax)?<BR>\n" );
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document.write( "Subtract the taxes from both totals and we have 2.10 and 5.15<BR>\n" );
document.write( "Let x = drinks; y = tacos<BR>\n" );
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document.write( "1x + 1y = 2.10<BR>\n" );
document.write( "and<BR>\n" );
document.write( "2x + 3y = 5.15<BR>\n" );
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document.write( "Mult 1st equation by 2 and subtract, solve for y<BR>\n" );
document.write( "2x + 3y = 5.15<BR>\n" );
document.write( "2x + 2y = 4.20<BR>\n" );
document.write( "-----------------subtract<BR>\n" );
document.write( "0x + y = .95 is the cost of a taco<BR>\n" );
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document.write( "I'll let you fiqure out the drink cost from the 1st equation<BR>\n" );
document.write( "Check your solutions in the 2nd equation.<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "(3) Given below are two equivalent systems of equations. Find the value of A and B.<BR>\n" );
document.write( "x +  2y =  2<BR>\n" );
document.write( "5x - 3y = -29<BR>\n" );
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document.write( "Solve the above sytem for x & y,<BR>\n" );
document.write( "Use elimination, mult the 1st eq by 3 and the 2nd equation by 2:<BR>\n" );
document.write( " 3x + 6y = 6<BR>\n" );
document.write( "10x - 6y = -58<BR>\n" );
document.write( "------------------add<BR>\n" );
document.write( "13x + 0y = -52<BR>\n" );
document.write( "x = -52/13<BR>\n" );
document.write( "x = -4<BR>\n" );
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document.write( "Find y using x + y = 2<BR>\n" );
document.write( "-4 + 2y = 2<BR>\n" );
document.write( "2y = 2 + 4<BR>\n" );
document.write( "y = 6/2<BR>\n" );
document.write( "y = + 3<BR>\n" );
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document.write( "Substitute -4 for x and +3 for y in the following to find a & b<BR>\n" );
document.write( "A(-4) + 5(3) = -9<BR>\n" );
document.write( "-4A = 15 = -9<BR>\n" );
document.write( "-4A = -9 - 15<BR>\n" );
document.write( "-4a = -24<BR>\n" );
document.write( "a = -24/-4<BR>\n" );
document.write( "a = + 6<BR>\n" );
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document.write( "Find B:<BR>\n" );
document.write( "-4 + B(3) = 8<BR>\n" );
document.write( "3B = 8 + 4<BR>\n" );
document.write( "B = 12/3<BR>\n" );
document.write( "B + +4<BR>\n" );
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document.write( "Did all this make sense to you??<BR>\n" );
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