document.write( "Question 1201382: Hi
\n" ); document.write( "The ratio of 20cent coins and 10cent coins was 4:7 respectively. After exchanging 8 20cent coins for 10cent coins the ratio became 2:11 . How much money did Bob have at first.
\n" ); document.write( "Thanks \n" ); document.write( "
Algebra.Com's Answer #835728 by Theo(13342)\"\" \"About 
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x = the number of 20 cent coins.
\n" ); document.write( "y = the number of 10 cent coins.
\n" ); document.write( "ratio of 20 cent coins to 10 cent coins is 4/7.
\n" ); document.write( "you get:
\n" ); document.write( "x/y = 4/7
\n" ); document.write( "after exchanging 8 twenty cent coins for ten cent coins, the ration becomes 2/11.
\n" ); document.write( "8 twenty cent coins is equal to 16 ten cent coins.
\n" ); document.write( "you get:
\n" ); document.write( "(x-8)/(y+16) = 2/11
\n" ); document.write( "in tyhe second equation, cross multiply to get:
\n" ); document.write( "(x-8)*11 = (y+16)*2
\n" ); document.write( "simplify to get:
\n" ); document.write( "11x-88 = 2y+32
\n" ); document.write( "since x/y = 4/7, solve for x to get:
\n" ); document.write( "x = 4y/7
\n" ); document.write( "replace x in the equation of 11x-88 = 2y+32 to get:
\n" ); document.write( "11*4y/7 - 88 = 2y + 32
\n" ); document.write( "simplify to get:
\n" ); document.write( "44y/7 - 88 = 2y + 32
\n" ); document.write( "add 88 to both sides of the equation to get:
\n" ); document.write( "44y/7 = 2y+120
\n" ); document.write( "multiply both sides of the equation by 7 to get:
\n" ); document.write( "44y = 14y + 840
\n" ); document.write( "subtract 14y from both sides of the equation to get:
\n" ); document.write( "30y = 840
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = 840/30 = 28
\n" ); document.write( "from the original equation of x/y = 4/7, rplace y with 28 to get:
\n" ); document.write( "x/28 = 4/7
\n" ); document.write( "multiply both sides of this equation by 28 to get:
\n" ); document.write( "x = 28*4/7 = 16
\n" ); document.write( "you have:
\n" ); document.write( "x = 16
\n" ); document.write( "y = 28
\n" ); document.write( "x/y = 16/28 = 4/7
\n" ); document.write( "(x-8)/(y+16) = 8/44 = 2/11
\n" ); document.write( "looks like the value of x = 16 and y = 28 are good.
\n" ); document.write( "they wanted to know how much money bob had at first.
\n" ); document.write( "at first he had 16 twenty cent coins and 28 ten cent coins.
\n" ); document.write( "the value would be 16 * .20 + 28 * .10 = 3.20 + 2.80 = 6.00
\n" ); document.write( "after he exchanged the coins, he should have the same amount, if i understood your problem correctly.
\n" ); document.write( "after the exchange, he had 8 twenty cent coins and 44 ten cent coins.
\n" ); document.write( "8 * .20 + 44 * .10 = 1.60 + 4.40 = 6.00, confirming that this is true.
\n" ); document.write( "your solution, as best i can determine, is he has $6.00 before and after the exchange.\r
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