document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173678>Question 173678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am a parent and trying to help my daugther could you help!<BR>\n" );
document.write( "1. Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out three times as many units of plywood as lumber. It makes a profit of $30 on a unit of lumber and $45 on a unit of plywood. How many of  each unit must be produced and sold in order to make a profit of $17160?\r<BR>\n" );
document.write( "\n" );
document.write( "Snooker Lumber must produce and sell__ units of lumber and__ units of plywood to make a profit of $17160.\r<BR>\n" );
document.write( "\n" );
document.write( "2. A disc jockey must play 16 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 13 min, how many 30-second commercials were played that hour? How many 60-second commercials?\r<BR>\n" );
document.write( "\n" );
document.write( " How many 30-second commercials were played that hour?<BR>\n" );
document.write( "  How many 60-second commercials were played that hour?\r<BR>\n" );
document.write( "\n" );
document.write( "3. A student makes a $9.50 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?<BR>\n" );
document.write( "    How many quarters are there in the change?<BR>\n" );
document.write( "    How many fifty-cent pieces are there in the change?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4. The perimeter of a rectangle is 80.m. The length is 7 m more than twice the width. Find the dimensions.<BR>\n" );
document.write( "  What is the length?   And Width?\r<BR>\n" );
document.write( "\n" );
document.write( "5. Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 60 points. They won 9 more games than they tied. How many wins and how many ties did the team have?<BR>\n" );
document.write( "   How many wins did the team have?<BR>\n" );
document.write( "   How many ties did the team have?<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128562 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=128562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> question number 1:<BR>\n" );
document.write( "-----      <BR>\n" );
document.write( " 1. Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out three times as many units of plywood as lumber. It makes a profit of $30 on a unit of lumber and $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $17160?<BR>\n" );
document.write( "Snooker Lumber must produce and sell__ units of lumber and__ units of plywood to make a profit of $17160.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer to question number 1:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "mill turns out 3 times as many units of plywood as lumber. (given)<BR>\n" );
document.write( "let a = amount of plywood<BR>\n" );
document.write( "let b = amount of lumber<BR>\n" );
document.write( "equation is:<BR>\n" );
document.write( "a = 3*b<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "total profit is 17160<BR>\n" );
document.write( "profit on one piece of plywood is 45 (given)<BR>\n" );
document.write( "profit on one piece of lumber is 30 (given)<BR>\n" );
document.write( "profit on b pieces of lumber is 30*b<BR>\n" );
document.write( "profit on a pieces of plywood is 45*a<BR>\n" );
document.write( "equation for total profit is:<BR>\n" );
document.write( "30*b + 45*a = 17160<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have 2 equations you need to solve simultaneously (same value for b and same value for a applies to both).<BR>\n" );
document.write( "those equations are:<BR>\n" );
document.write( "a = 3*b<BR>\n" );
document.write( "30*b + 45*a = 17160<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since you know a = 3*b, you can substitute 3*b for a to get:<BR>\n" );
document.write( "30*b + 45*(3*b) = 17160<BR>\n" );
document.write( "this equation becomes:<BR>\n" );
document.write( "30*a + 135*b = 17160<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "165*b = 17160<BR>\n" );
document.write( "divide both sides of equation by 165 to get:<BR>\n" );
document.write( "b = 17160/165 = 104<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "b = 104<BR>\n" );
document.write( "you know that a = 3*b, so<BR>\n" );
document.write( "a = 3*104 = 312<BR>\n" );
document.write( "you now have:<BR>\n" );
document.write( "b = 104<BR>\n" );
document.write( "a = 312<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute in your profit equation to get:<BR>\n" );
document.write( "30*b + 45*a = 17160<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "30*104 + 45*312 = 17160<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "3120 + 14040 = 17160<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "both equations are satisfied (they are true when you substitute the values for a and b).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a = 3*b<BR>\n" );
document.write( "312 = 3*104 (true)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "30*b + 45*a = 17160 (shown to be true just above).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer to the question is:<BR>\n" );
document.write( "the mill must produce and sell 312 units of plywood and 104 units of lumber to make a profit of 17160.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "question number 2:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "2. A disc jockey must play 16 commercial spots during 1 hour of a radio show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during 1 hour is 13 min, how many 30-second commercials were played that hour? How many 60-second commercials?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer to question number 2:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let a = number of 30 second commercial<BR>\n" );
document.write( "let b = number of 60 second commercial<BR>\n" );
document.write( "total time for commercials is 13 minutes * 60 seconds per minute = 780 seconds.<BR>\n" );
document.write( "first equation for total time used is:<BR>\n" );
document.write( "30*a + 60*b = 780<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "total number of commercials is 16<BR>\n" );
document.write( "second equation for total number of commercials used is:<BR>\n" );
document.write( "a + b = 16<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this can also be solved by substitution same as in question number 1.<BR>\n" );
document.write( "solve for a in the second equation:<BR>\n" );
document.write( "a + b = 16<BR>\n" );
document.write( "subtract b from both sides:<BR>\n" );
document.write( "a = 16 - b<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute 16-b for a in the first equation:<BR>\n" );
document.write( "30*a + 60*b = 780 <BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( "30*(16-b) + 60*b = 780<BR>\n" );
document.write( "expand:<BR>\n" );
document.write( "30*16 - 30*b + 60*b = 780<BR>\n" );
document.write( "combine like terms:<BR>\n" );
document.write( "30*16 + 30*b = 780<BR>\n" );
document.write( "subtract 30*16 from both sides:<BR>\n" );
document.write( "30*b = 780 - (30*16)<BR>\n" );
document.write( "expand:<BR>\n" );
document.write( "30*b = 780 - 480<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "30*b = 300<BR>\n" );
document.write( "divide both sides by 30:<BR>\n" );
document.write( "b = 300/30 <BR>\n" );
document.write( "b = 10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since b = 10, and a + b = 16, then:<BR>\n" );
document.write( "a = 6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "a = 6<BR>\n" );
document.write( "b = 10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute for a and b in first equation:<BR>\n" );
document.write( "30*a + 60*b = 780<BR>\n" );
document.write( "30*6 + 60*10 = 780<BR>\n" );
document.write( "180 + 600 = 780<BR>\n" );
document.write( "780 = 780<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equations are good<BR>\n" );
document.write( "answer to question number 2 is:<BR>\n" );
document.write( "number of 30 second commercials is 6.<BR>\n" );
document.write( "number of 60 second commercials is 10.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "question number 3:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "3. A student makes a $9.50 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?<BR>\n" );
document.write( "How many quarters are there in the change?<BR>\n" );
document.write( "How many fifty-cent pieces are there in the change?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer to question number 3:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the change is 20.00 - 9.50 = 10.50<BR>\n" );
document.write( "let a = # quarters<BR>\n" );
document.write( "let b = # fifty cent pieces<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "number of coins is 30:<BR>\n" );
document.write( "a + b = 30<BR>\n" );
document.write( "total change is 10.50<BR>\n" );
document.write( ".25*a + .5*b = 10.5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "two equations are:<BR>\n" );
document.write( "a + b = 30<BR>\n" );
document.write( ".25*a + 5*b = 10.5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we can use substitution as in questions 1 and 2 above, or we can solve as two simultaneous equations by manipulating the equations so one of the unknowns drops out allowing us to solve for the other unknown.<BR>\n" );
document.write( "we'll do it the second way this time.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "two equations are:<BR>\n" );
document.write( "a + b = 30<BR>\n" );
document.write( ".25*a + .5*b = 10.5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply the second equation by 4:<BR>\n" );
document.write( "a + b = 30<BR>\n" );
document.write( "a + 2b = 42<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract first equation from second equation to get:<BR>\n" );
document.write( "a-a + 2b-b = 42-30<BR>\n" );
document.write( "b = 12<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if b = 12, then a = 18 because a + b = 30<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "a = 18<BR>\n" );
document.write( "b = 12<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute in the second equation to see if we get the right answer:<BR>\n" );
document.write( ".25*a + .5*b = 10.5<BR>\n" );
document.write( ".25*18 + .5*12 = 10.5<BR>\n" );
document.write( "4.5 + 6 = 10.5<BR>\n" );
document.write( "10.5 = 10.5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "values are good<BR>\n" );
document.write( "answer to question number 3 is:<BR>\n" );
document.write( "there are 12 fifty cent pieces in the change<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "question number 4:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "4. The perimeter of a rectangle is 80.m. The length is 7 m more than twice the width. Find the dimensions.<BR>\n" );
document.write( "What is the length? And Width?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer to question number 4:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let a = length<BR>\n" );
document.write( "let b = width<BR>\n" );
document.write( "perimeter = 80 meters<BR>\n" );
document.write( "length is 7 meters more than twice the width.<BR>\n" );
document.write( "equation for that is:<BR>\n" );
document.write( "a = 2*b + 7<BR>\n" );
document.write( "formula for perimeter is:<BR>\n" );
document.write( "2*a = 2*b = 80<BR>\n" );
document.write( "substitute 2*b+7 for a to get:<BR>\n" );
document.write( "2*(2*b+7) + 2*b = 80<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "4*b + 14 + 2*b = 80<BR>\n" );
document.write( "combine like terms:<BR>\n" );
document.write( "6*b + 14 = 80<BR>\n" );
document.write( "subtract 14 from both sides:<BR>\n" );
document.write( "6*b = 66<BR>\n" );
document.write( "b = 11<BR>\n" );
document.write( "a = 2*b + 7<BR>\n" );
document.write( "a = 2*11 + 7<BR>\n" );
document.write( "a = 29<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute in perimeter equation to prove this is true.<BR>\n" );
document.write( "2*a + 2*b = 80<BR>\n" );
document.write( "2*29 + 2*11 = 80<BR>\n" );
document.write( "58 + 22 = 80<BR>\n" );
document.write( "80 = 80<BR>\n" );
document.write( "equation is true<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer to question # 4 is:<BR>\n" );
document.write( "length is 29<BR>\n" );
document.write( "width is 11<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "question number 5:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "5. Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 60 points. They won 9 more games than they tied. How many wins and how many ties did the team have?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer to question number 5:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "w = number of wins<BR>\n" );
document.write( "t = number of ties<BR>\n" );
document.write( "they won 9 more games than they tied:<BR>\n" );
document.write( "w = t+9<BR>\n" );
document.write( "2 points for a win<BR>\n" );
document.write( "1 point for a tie<BR>\n" );
document.write( "total points = 60:<BR>\n" );
document.write( "2w + 1t = 60<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since w = t+9, substitute in total points equation to get:<BR>\n" );
document.write( "2w + 1t = 60<BR>\n" );
document.write( "2(t+9) + 1t = 60<BR>\n" );
document.write( "2t + 18 + 1t = 60<BR>\n" );
document.write( "3t + 18 = 60<BR>\n" );
document.write( "3t = 42 (you subtract 18 from both sides)<BR>\n" );
document.write( "t = 14 (you divide both sides by 3)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "w = 23 (w = t+9)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "w = 23<BR>\n" );
document.write( "t = 14<BR>\n" );
document.write( "substitute in equation for total points:<BR>\n" );
document.write( "2w + 1t = 60<BR>\n" );
document.write( "2*(23) + 1*(14) = 60<BR>\n" );
document.write( "46 + 14 = 60<BR>\n" );
document.write( "60 = 60<BR>\n" );
document.write( "equeation is good.<BR>\n" );
document.write( "answer to question number 5 is:<BR>\n" );
document.write( "the team had 23 wins and 14 ties<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );