document.write( "Question 1201507: The ratio of Karen's beads to Sarah's beads is 7:5 . When Sarah gives 48 beads to Karen, she has 1/3 of the number of beads Karen has. During a game, Karen lost some beads to Sarah. As a result, Karen had 1/5 as many beads as Sarah. How many beads did Karen lose? \n" ); document.write( "
Algebra.Com's Answer #835900 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Answer: 120\r
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\n" ); document.write( "\n" ); document.write( "Explanation:\r
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\n" ); document.write( "\n" ); document.write( "I'll break the instructions into three parts
  1. The ratio of Karen's beads to Sarah's beads is 7:5
  2. When Sarah gives 48 beads to Karen, she has 1/3 of the number of beads Karen has.
  3. During a game, Karen lost some beads to Sarah. As a result, Karen had 1/5 as many beads as Sarah.
Part 1
\n" ); document.write( "Ratio of Karen's beads to Sarah's beads is 7:5
\n" ); document.write( "Scale each part by x to get 7x:5x
\n" ); document.write( "x is some positive whole number
\n" ); document.write( "7x = Karen's starting count
\n" ); document.write( "5x = Sarah's starting count\r
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\n" ); document.write( "\n" ); document.write( "Part 2
\n" ); document.write( "Sarah gives 48 beads to Karen
\n" ); document.write( "Sarah's count of 5x drops to 5x-48
\n" ); document.write( "Karen's count of 7x increases to 7x+48
\n" ); document.write( "After these adjustments, we know that Sarah has 1/3 that Karen does.
\n" ); document.write( "In other words, Karen has triple that of Sarah.
\n" ); document.write( "Karen = 3*Sarah
\n" ); document.write( "7x+48 = 3*(5x-48)
\n" ); document.write( "7x+48 = 15x-144
\n" ); document.write( "7x-15x = -144-48
\n" ); document.write( "-8x = -192
\n" ); document.write( "x = -192/(-8)
\n" ); document.write( "x = 24
\n" ); document.write( "Then,
\n" ); document.write( "Karen's start count = 7x = 7*24 = 168
\n" ); document.write( "Sarah's start count = 5x = 5*24 = 120\r
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\n" ); document.write( "\n" ); document.write( "Check so far:
\n" ); document.write( "Karen and Sarah start with 168 and 120 beads respectively.
\n" ); document.write( "Sarah gives 48 beads, so,
\n" ); document.write( "Karen: 168+48 = 216
\n" ); document.write( "Sarah: 120-48 = 72
\n" ); document.write( "Their ratio is Sarah/Karen = 72/216 = 1/3 which confirms we did things correctly so far.\r
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\n" ); document.write( "\n" ); document.write( "Part 3
\n" ); document.write( "\"During a game, Karen lost some beads to Sarah. As a result, Karen had 1/5 as many beads as Sarah. \"\r
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\n" ); document.write( "\n" ); document.write( "L = amount of beads lost
\n" ); document.write( "Karen's count goes from 168 to 168-L
\n" ); document.write( "Sarah's count goes from 120 to 120+L\r
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\n" ); document.write( "\n" ); document.write( "Then,
\n" ); document.write( "Karen = (1/5)*Sarah
\n" ); document.write( "Sarah = 5*Karen
\n" ); document.write( "120+L = 5*(168-L)
\n" ); document.write( "120+L = 840-5L
\n" ); document.write( "L+5L = 840-120
\n" ); document.write( "6L = 720
\n" ); document.write( "L = 720/6
\n" ); document.write( "L = 120
\n" ); document.write( "Karen lost 120 beads to Sarah\r
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "Karen lost 120 beads, so she has 168-120 = 48 beads left.
\n" ); document.write( "Sarah gained those 120 beads, so she has 120+120 = 240 beads
\n" ); document.write( "Their ratio is Karen/Sarah = 48/240 = 1/5
\n" ); document.write( "The final answer is confirmed.
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