document.write( "Question 103649: A collection of dimes and quarters amounts to $1.80. There are 12 coins in all. How many of each coin are there? \n" ); document.write( "
Algebra.Com's Answer #75362 by doukungfoo(195)\"\" \"About 
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lets call the number of dimes d
\n" ); document.write( "and the number of quarters q
\n" ); document.write( "Ok so just to be clear we have:
\n" ); document.write( "the number of dimes = d
\n" ); document.write( "the number of quarters = q
\n" ); document.write( "Now lets look at what we know:
\n" ); document.write( "Given: there are 12 coins in all
\n" ); document.write( "write an equation using d and q to express this fact
\n" ); document.write( "d + q = 12
\n" ); document.write( "What else do we know?
\n" ); document.write( "Given: a collection of dimes and quarters amounts to $1.80
\n" ); document.write( "and we should know that a quarter equals 0.25 cents
\n" ); document.write( "and a dime equal 0.10 cents
\n" ); document.write( "Again use d and q to write and equations to express this information
\n" ); document.write( "0.10d + 0.25q = 1.80
\n" ); document.write( "In other words:
\n" ); document.write( ".10 times the number of dimes plus .25 times the number of quarters equals $1.80
\n" ); document.write( "ok now we have a system of equations that we can use to solve for d and q
\n" ); document.write( "First take the equation d + q = 12 and set it equal to d
\n" ); document.write( "d = 12 - q
\n" ); document.write( "Now since we have shown that d equals 12-q lets use that in the second equation
\n" ); document.write( "0.10d + 0.25q = 1.80
\n" ); document.write( "0.10(12-q) + 0.25q = 1.80
\n" ); document.write( "1.2 - .1q + .25q = 1.80
\n" ); document.write( "1.2 + .15q = 1.80
\n" ); document.write( ".15q = .60
\n" ); document.write( ".15q/.15 = .60/.15
\n" ); document.write( "q = 4
\n" ); document.write( "Answer: there are 4 quarters in the collection
\n" ); document.write( "Now use this to find the number of dimes
\n" ); document.write( "d + q = 12
\n" ); document.write( "d + 4 = 12
\n" ); document.write( "d = 12 - 4
\n" ); document.write( "d = 8
\n" ); document.write( "Answer: there are 8 dimes in the collection
\n" ); document.write( "Check answers by trying them in both equations
\n" ); document.write( "d + q = 12
\n" ); document.write( "8 + 4 = 12
\n" ); document.write( "12 = 12
\n" ); document.write( "-----------------
\n" ); document.write( "0.10d + 0.25q = 1.80
\n" ); document.write( "0.10(8) + 0.25(4) = 1.80
\n" ); document.write( "0.80 + 1.00 = 1.80
\n" ); document.write( "1.80 = 1.80\r
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