document.write( "Question 1184459: Gillian and Ben had a total of 4850 toys. Ben have 3/7 of his toys to Gillian. She then gave 1/3 of here toys to Ben. The ratio of the number of toys Gillian left to the number of toys Ben left was 2:3.
\n" ); document.write( "a) How many toys did Gillian have at the end?
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\n" ); document.write( "\n" ); document.write( "Dear teachers, can help me how to do this? Is ratio working backwards I think. \n" ); document.write( "
Algebra.Com's Answer #815085 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        Gillian  and  Ben had a total of  4850  toys. \r
\n" ); document.write( "\n" ); document.write( "        Ben  \"cross%28have%29\" GAVE  3/7  of his toys to  Gillian. \r
\n" ); document.write( "\n" ); document.write( "        She then gave  1/3  of  \"cross%28here%29\"  HER  toys to  Ben. \r
\n" ); document.write( "\n" ); document.write( "        The ratio of the number of toys  Gillian left to the number of toys  Ben \"cross%28left%29\"  finally had  was  2:3.\r
\n" ); document.write( "\n" ); document.write( "              a)   How many toys did  Gillian have at the end?\r
\n" ); document.write( "\n" ); document.write( "              b)   How many toys did  Ben have at first?
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\n" ); document.write( "\n" ); document.write( "I will solve the problem using backward solution method.\r
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\n" ); document.write( "\n" ); document.write( "To make the solution totally clear, I will present / (will re-tell) the problem's description in steps.\r
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document.write( "    1.  At the start, the total number of toys was 4850.\r\n" );
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document.write( "    2.  Ben gave 3/7 of his toys to Gilian.\r\n" );
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document.write( "    3.  Gilian then gave 1/3 of her toys to Ben.\r\n" );
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document.write( "    4.  After that, the ratio of Gilian's toys to Ben toys was 2:3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "                At this point, I start my solution.\r
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document.write( "Notice that, althought Gilian and Ben exchanged toys, the total number of toys remained 4850, with no change.\r\n" );
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document.write( "So, at the final step 4, there were totaly 4850 toys in the ratio Gilian to Ben as 2:3.\r\n" );
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document.write( "It means, there were 5 equal parts of toys, each part counted  4850/5 = 970 toys,\r\n" );
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document.write( "and Gilian had 2 such parts, or 2*970 = 1940 toys, while Ben had 3 such parts, or 3*970 = 2910 toys.\r\n" );
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document.write( "In particular, we just know the ANSWER to question (a):  Gilian had 1940 toys at the end.\r\n" );
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document.write( "Next, the last action that Gilian did was giving 1/3 of her toys to Ben.\r\n" );
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document.write( "    HENCE, her final number of toys, 1940, is 2/3 of what she had before this giving.\r\n" );
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document.write( "    So, we conclude that before giving to Ben, Gilian had  (3/2)*1940 = 2910 toys.\r\n" );
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document.write( "    Again, immediately before step 3, Gilian had 2910 toys.\r\n" );
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document.write( "    Hence, immediately before step 3, Ben had the rest  4850 - 2910 = 1940 toys.\r\n" );
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document.write( "Thus we analysed the final stage and then restored from the condition, that immediately before step 3,\r\n" );
document.write( "Gilian had 2910 toys, while Ben had 1940 toys.\r\n" );
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document.write( "Next, moving back, we know that after step 2, Ben had 1940 toys; Gilian had 2910 toys.\r\n" );
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document.write( "    In other words, after giving Gilian 3/7 of his toys at the step 2, Ben left with 1940 toys; it is 4/7 what he had before his giving.\r\n" );
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document.write( "    HENCE, before this giving, Ben had 7/4*1940 = 3395 toys and Gilian had the rest 4850-3395 = 1455 toys.\r\n" );
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document.write( "    Again, immediately before step 2, Ben had 3395 toys anad Gilian had the rest 1455 toys.\r\n" );
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document.write( "It gives the ANSWER to question (a): at first, Ben had 3395 toys.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Yes,  I solved the problem using the backward solution method,\r
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