document.write( "Question 1065268: Moolah has 27 coins that are all dimes and quarters. The value of the coins is $4.35. How many dimes and how many quarters does Moolah have? \n" ); document.write( "

Algebra.Com's Answer #680406 by KMST(5328) $\"\"$ $\"About$

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THE FIFTH GRADER APPROACH:
\n" ); document.write( "We know that 17 quarters make $4.25,
\n" ); document.write( "so 17 quarters + 1 dime = 18 coins makes $4.35.
\n" ); document.write( "However, with that combination we are
\n" ); document.write( "27-18=9 coins short of the required number of coins.
\n" ); document.write( "We also know that $0.50 can be made with 5 dimes or with 2 quarters.
\n" ); document.write( "Replacing 2 quarters with 5 dimes increases the number of coins by
\n" ); document.write( "5-2=3 , but does not alter the value of the set of coins.
\n" ); document.write( "Since the combination of 17 quarters and 1 dime was 9 coins short,
\n" ); document.write( "we can make 9÷3=3 swaps of 5 dimes for 2 quarters and end up with
\n" ); document.write( "2×3=6 less quarters, and
\n" ); document.write( "5×3=15 more dimes.
\n" ); document.write( "Then we would have
\n" ); document.write( "17-6= $\"highlight%2811%29\"$ quarters and
\n" ); document.write( "1+15= $\"highlight%2816%29\"$ dimes.
\n" ); document.write( "The total amount would still be $4.35,
\n" ); document.write( "but the number of coins would be the required
\n" ); document.write( "11+16=27 .
\n" ); document.write( "
\n" ); document.write( "AS AN ALGEBRA EXERCISE:
\n" ); document.write( "You start by defining one variable (or two):
\n" ); document.write( " $\"x\"$ = number of quarters
\n" ); document.write( "If you would like to use two variables you would also define
\n" ); document.write( " $\"y\"$ = number of dimes,
\n" ); document.write( "and then you would write
\n" ); document.write( " $\"x%2By=27\"$ as one of your equations.
\n" ); document.write( "From there, solving for $\"y\"$ you would have
\n" ); document.write( " $\"y=27-x\"$ as the number of dimes.
\n" ); document.write( "If you rather use just one variable,
\n" ); document.write( "you would just say directly that
\n" ); document.write( " $\"27-x\"$ = number of dimes.
\n" ); document.write( "Your other equation would be
\n" ); document.write( "the one relating the numbers of coins
\n" ); document.write( "to the value in $ :
\n" ); document.write( " $\"0.25x%2B0.10y=4.35\"$ if you use two variables,
\n" ); document.write( "or $\"0.25x%2B0.10%2827-x%29=4.35\"$ .
\n" ); document.write( "The equation above is what you get substituting
\n" ); document.write( " $\"27-x\"$ for $\"y\"$ in the equation with two variables.
\n" ); document.write( "It is also what you would write directly
\n" ); document.write( "if you are using just one variable.
\n" ); document.write( "Solving:
\n" ); document.write( " $\"0.25x%2B0.10%2827-x%29=4.35\"$
\n" ); document.write( " $\"0.25x%2B2.70-0.10x=4.35\"$
\n" ); document.write( " $\"0.15x%2B2.70=4.35\"$
\n" ); document.write( " $\"0.15x=4.35-2.70\"$
\n" ); document.write( " $\"0.15x=1.65\"$
\n" ); document.write( "Multiplying both sides of the equal sign times 20,
\n" ); document.write( "we get $\"3x=33\"$ ,and we do not have to deal with decimals.
\n" ); document.write( "If we had multiplied times 10p, we would have
\n" ); document.write( " $\"15x=165\"$ , with is equivalent.
\n" ); document.write( "From either one, we get $\"highlight%28x=11%29\"$
\n" ); document.write( "for the number of quarters.
\n" ); document.write( "After that, we calculate the number of dimes as
\n" ); document.write( " $\"27-x=27-11=highlight%2816%29\"$ ,
\n" ); document.write( "or as $\"y=27-x=27-11=highlight%2816%29\"$ . \n" ); document.write( "

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