document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208367>Question 1208367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "If Simon gave 30% of his sweets to Terry they will have the same number of sweets.  If Simon gave 250 sweets to Terry, Terry will 80% more sweets than Simon. How many sweets does Simon have.  </SPAN>\n" );
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document.write( "Answer: <font color=red>500</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "x = number of sweets Simon starts with<BR>\n" );
document.write( "y = number of sweets Terry starts with\r<BR>\n" );
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document.write( "Scenario 1. Simon gives 30% of his sweets to Terry. After this they end up with the same number of sweets.\r<BR>\n" );
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document.write( "Scenario 2. Simon gives 250 sweets to Terry. Afterward, Terry will have 80% more sweets compared to Simon.\r<BR>\n" );
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document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Scenario 1</TD><TD >Before</TD><TD >After</TD></tr><tr><TD >Simon</TD><TD >x</TD><TD >0.7x</TD></tr><tr><TD >Terry</TD><TD >y</TD><TD >y+0.3x</TD></tr>\n" );
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document.write( "Since they end up with the same number of sweets, we can say 0.7x = y+0.3x<BR>\n" );
document.write( "Solve for y to get y = 0.4x<BR>\n" );
document.write( "We'll use this later.\r<BR>\n" );
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document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Scenario 2</TD><TD >Before</TD><TD >After</TD></tr><tr><TD >Simon</TD><TD >x</TD><TD >x-250</TD></tr><tr><TD >Terry</TD><TD >y</TD><TD >y+250</TD></tr>\n" );
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document.write( "At the end of this scenario, Terry has 80% more sweets compared to Simon.<BR>\n" );
document.write( "Think of it like this<BR>\n" );
document.write( "TerrysCount = SimonsCount + 80% of SimonsCount<BR>\n" );
document.write( "TerrysCount = SimonsCount + 0.8*SimonsCount<BR>\n" );
document.write( "TerrysCount = (1 + 0.8)*SimonsCount<BR>\n" );
document.write( "TerrysCount = 1.8*SimonsCount<BR>\n" );
document.write( "Or think of \"Terry has 80% more\" as \"Terry's count is 180% of Simon's count\". 180% then converts to the decimal form 1.8\r<BR>\n" );
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document.write( "Based on that template, we can then say,<BR>\n" );
document.write( "TerrysCount = 1.8*SimonsCount<BR>\n" );
document.write( "y+250 = 1.8*(x-250)<BR>\n" );
document.write( "0.4x+250 = 1.8*(x-250) .............. plug in y = 0.4x<BR>\n" );
document.write( "0.4x+250 = 1.8x-450 <BR>\n" );
document.write( "1.8x-0.4x = 250+450 <BR>\n" );
document.write( "1.4x = 700<BR>\n" );
document.write( "x = 700/1.4<BR>\n" );
document.write( "x = <font color=red>500</font><BR>\n" );
document.write( "Simon started with <font color=red>500</font> sweets.<BR>\n" );
document.write( "y = 0.4x = 0.4*500 = 200 is the number of sweets Terry started with.\r<BR>\n" );
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document.write( "--------------------------------------\r<BR>\n" );
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document.write( "Let's check the answer. <BR>\n" );
document.write( "To do that we go through each scenario. <BR>\n" );
document.write( "I'll update each previous table to plug in the mentioned x and y values. <BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Scenario 1</TD><TD >Before</TD><TD >After</TD></tr><tr><TD >Simon</TD><TD >500</TD><TD >350</TD></tr><tr><TD >Terry</TD><TD >200</TD><TD >350</TD></tr>\n" );
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document.write( "Both end up with an equal number of candies (each with 350).<BR>\n" );
document.write( "This confirms scenario 1.\r<BR>\n" );
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document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Scenario 2</TD><TD >Before</TD><TD >After</TD></tr><tr><TD >Simon</TD><TD >500</TD><TD >250</TD></tr><tr><TD >Terry</TD><TD >200</TD><TD >450</TD></tr>\n" );
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document.write( "Divide Terry's new count over Simon's new count to get 450/250 = 1.8 to show that Terry has 80% more compared to Simon.<BR>\n" );
document.write( "Or you can notice that Terry has 450-250 = 200 more candies compared to Terry, and 200/250 = 0.80 = 80%\r<BR>\n" );
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document.write( "Both scenarios are confirmed. This confirms the answer.<BR>\n" );
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