document.write( "Question 874334: I need to know how to set up this equation. Please explain the logic behind how you set it up. A purse contains $3.75 in 5 cent and 20 cent coins. there are 33 coins all together. How much of each coin is there? \n" ); document.write( "
Algebra.Com's Answer #527440 by nerdybill(7384)\"\" \"About 
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A purse contains $3.75 in 5 cent and 20 cent coins. there are 33 coins all together. How much of each coin is there?
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\n" ); document.write( "Let x = number of 5 cent coins
\n" ); document.write( "and y = number of 20 cent coins
\n" ); document.write( "then
\n" ); document.write( "from \"A purse contains $3.75\" we get:
\n" ); document.write( ".05x + .20y = 3.75 (equation 1)
\n" ); document.write( "and from \"there are 33 coins\" we get:
\n" ); document.write( "x + y = 33 (equation 2)
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\n" ); document.write( "Solve equation 2 for y:
\n" ); document.write( "x + y = 33
\n" ); document.write( "y = 33-x
\n" ); document.write( ".
\n" ); document.write( "Substitute above into equation 1 and solve for x:
\n" ); document.write( ".05x + .20y = 3.75
\n" ); document.write( ".05x + .20(33-x) = 3.75
\n" ); document.write( ".05x + 6.60 - .20x = 3.75
\n" ); document.write( "6.60 - .15x = 3.75
\n" ); document.write( "-.15x = -2.85
\n" ); document.write( "x = -2.85/(-.15)
\n" ); document.write( "x = 19 (number of 5 cent coins)
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\n" ); document.write( "number of 20 cent coins:
\n" ); document.write( "y = 33-x = 33-19 = 14
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