document.write( "Question 1209504: Hi
\n" ); document.write( "Jamie spent 3/4 of her money on 3 books of the same price. Grace spent 5/9 of her money on 2 diaries. They were each left with an equal amount of money. One book cost $3.30 more than one diary. How much money did they have altogether. \n" ); document.write( "
Algebra.Com's Answer #849013 by ikleyn(52852)\"\" \"About 
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\n" ); document.write( "Jamie spent 3/4 of her money on 3 books of the same price.
\n" ); document.write( "Grace spent 5/9 of her money on 2 diaries.
\n" ); document.write( "They were each left with an equal amount of money.
\n" ); document.write( "One book \"highlight%28cross%28cost%29%29\" costs $3.30 more than one diary.
\n" ); document.write( "How much money did they have altogether.
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document.write( "Let x be the price of one diary, in dollars.\r\n" );
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document.write( "Then the price of one book is (x+3.30) dollars, according to the problem.\r\n" );
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document.write( "Jamie spent 3/4 of her money and bought 3 books.\r\n" );
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document.write( "Hence, one book costs 1/4 of Jamie's money.\r\n" );
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document.write( "But 1/4 of Jamie's money is exactly the amount which left in Jamie's possession..\r\n" );
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document.write( "So, we conclude that Jamie left (x+3.30) dollars.\r\n" );
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document.write( "    +-----------------------------------------------------------------------------+\r\n" );
document.write( "    |   OK, it is fine.  So, (x+3.30) dollars is the left side of the equation,   |\r\n" );
document.write( "    |             which we are going to built to solve the problem.               |\r\n" );
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document.write( "Now let's calculate on the Grace side.\r\n" );
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document.write( "Grace spent 2x dollars, which is  5/9 of her starting money.  Hence, Grace's starting money was  \r\n" );
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document.write( "    \"%289%2F5%29%2A%282x%29\" = \"%2818%2F5%29x\".\r\n" );
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document.write( "From it, we should take  4/9  of  \"%2818%2F5%29x\"  to calculate the part of Grace's money which left.  So,\r\n" );
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document.write( "    Grace's money left =  \"%284%2F9%29%2A%2818%2F5%29x\" = \"%28%284%2A2%29%2F5%29x\" = \"%288%2F5%29x\"\r\n" );
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document.write( "    +----------------------------------------------------+\r\n" );
document.write( "    |   Thus, Grace's money left is  (8/5)*x  dollars.   |\r\n" );
document.write( "    |   It is the right side of our equation for         |\r\n" );
document.write( "    |                money left.                         |\r\n" );
document.write( "    +----------------------------------------------------+\r\n" );
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document.write( "And now the equation for  money left  is\r\n" );
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document.write( "    x + 3.30 = \"%288%2F5%29x\".    ( ! ! ! - here three exclamation signs express my delight)\r\n" );
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document.write( "To solve, multiply by 5 both sides of this equation\r\n" );
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document.write( "    5x + 5*3.30 = 8x\r\n" );
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document.write( "    5*3.30 = 8x - 5x\r\n" );
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document.write( "    5*3.30 = 3x\r\n" );
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document.write( "    x = \"%285%2A3.30%29%2F3\" = 5*1.10 = 5.50.\r\n" );
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document.write( "So, one diary costs 5.50 dollars and one book costs $3.30 more,  or  5.50+3.30 = 8.80 dollars.\r\n" );
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document.write( "        Now we are in the finish line.\r\n" );
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document.write( "Jamie spent 3*8.80 = 26.40 dollars.  It is 3/4 of her starting money.\r\n" );
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document.write( "Hence, Jamie's starting money was  \"%284%2F3%29%2A26.40\" = 35.20 dollars.\r\n" );
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document.write( "Grace spent 2*5.50 = 11 dollars.  It is 5/9 of her starting money.\r\n" );
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document.write( "Hence, Grace's starting money was  \"%289%2F5%29%2A11\" = 19.80 dollars.\r\n" );
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document.write( "Thus the starting money of two girls, altogether, was  35.20 + 19.80 = 55 dollars.\r\n" );
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document.write( "ANSWER.  Initially, the girls had  55 dollars, altogether.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "This problem is nice. It teaches to think and forces to think.\r
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\n" ); document.write( "\n" ); document.write( "Perhaps, some tutors will come, offering other (more shorter or more \"iron language\" solutions).\r
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\n" ); document.write( "\n" ); document.write( "I wrote my solution trying to make it accessible for as young students
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\n" ); document.write( "\n" ); document.write( "Ignore the post by @CPhill, since it exploits wrong logic.\r
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\n" ); document.write( "\n" ); document.write( "Comment from student: Hi ikleyn I am glad you enjoyed this problem. I honestly thought I was going to get a roasting
\n" ); document.write( "for posting a badly worded question. This textbook my son uses for extra work is very good,
\n" ); document.write( "however some of the questions...the wording makes your head spin. 😀 you are a GREAT TUTOR\r
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\n" ); document.write( "\n" ); document.write( "My response: I am glad to see your adequate reaction, which rarely happens at this forum.\r
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\n" ); document.write( "\n" ); document.write( "Can you, PLEASE, post me the name of the textbook your son uses for extra work.\r
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\n" ); document.write( "\n" ); document.write( "Thank you in advance.\r
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\n" ); document.write( "\n" ); document.write( ". . . . . . . . . . . . . . . .\r
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\n" ); document.write( "\n" ); document.write( "Please, do not afraid my criticism. After it, all things become better:\r
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\n" ); document.write( "\n" ); document.write( "        - Bad/wrong problem formulations obtain their true rank, which they deserve;\r
\n" ); document.write( "\n" ); document.write( "        - obscure formulations/tasks become clear, \r
\n" ); document.write( "\n" ); document.write( "        - and all reasonable tasks become solved and explained.\r
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