document.write( "Question 720267: I have a mason jar full of coins. Your task is to calculate exactly how many pennies, nickels, dimes and quarters are in the jar. There are 513 coins in the jar. The combined weight of the jar and the coins is 1779 grams. The number of pennies in the jar is twice the sum of the nickels, dimes, and quarters. Quarters weigh 5.8 grams, dimes weigh 2.3 grams, nickels weigh 5.0 grams and pennies weigh 2.5 grams. The jar weighs 301 grams empty. \n" ); document.write( "

Algebra.Com's Answer #441768 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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calculate exactly how many pennies, nickels, dimes and quarters are in the jar.
\n" ); document.write( " There are 513 coins in the jar.
\n" ); document.write( "The combined weight of the jar and the coins is 1779 grams.
\n" ); document.write( " The number of pennies in the jar is twice the sum of the nickels, dimes, and quarters.
\n" ); document.write( " Quarters weigh 5.8 grams, dimes weigh 2.3 grams, nickels weigh 5.0 grams and pennies weigh 2.5 grams.
\n" ); document.write( " The jar weighs 301 grams empty.
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement;
\n" ); document.write( "\"There are 513 coins in the jar.
\n" ); document.write( "p + n + d + q = 513
\n" ); document.write( ":
\n" ); document.write( "\"The number of pennies in the jar is twice the sum of the nickels, dimes, and quarters.\"
\n" ); document.write( "p = 2(n+d+q)
\n" ); document.write( "divide both sides by 2
\n" ); document.write( ".5p = (n+d+q)
\n" ); document.write( "then replace n+d+q with .5p
\n" ); document.write( "p + .5p = 513
\n" ); document.write( "1.5p = 513
\n" ); document.write( " p = 513/1.5
\n" ); document.write( " p = 342 pennies
\n" ); document.write( ":
\n" ); document.write( "\"The combined weight of the jar and the coins is 1779 grams.
\n" ); document.write( "Quarters weigh 5.8 grams, dimes weigh 2.3 grams, nickels weigh 5.0 grams and pennies weigh 2.5 grams. The jar weighs 301 grams empty.\"
\n" ); document.write( "2.5(342) + 5n + 2.3d + 5.8q = 1779 - 301
\n" ); document.write( "855 + 5n + 2.3d + 5.8q = 1478
\n" ); document.write( "5n + 2.3d + 5.8q = 1478 - 855
\n" ); document.write( "5n + 2.3d + 5.8q = 623
\n" ); document.write( "and we know
\n" ); document.write( "n + d + q = 513 - 342
\n" ); document.write( "n + d + q = 171
\n" ); document.write( "multiply by 5 and subtract weight equation
\n" ); document.write( "5n + 5d + 5q = 855
\n" ); document.write( "5n+2.3d+5.8q = 623
\n" ); document.write( "-------------------subtracting eliminates n
\n" ); document.write( "2.7d - .8q = 232
\n" ); document.write( "2.7d = .8q + 232
\n" ); document.write( "Divide by 2.7
\n" ); document.write( "d = $\".8%2F2.7\"$ q + $\"232%2F2.7\"$
\n" ); document.write( "Using the table of this equation on a Ti83, came up with integer values for d and q
\n" ); document.write( "d = 96
\n" ); document.write( "q = 34
\n" ); document.write( "Find n
\n" ); document.write( "n + 96 + 34 = 171
\n" ); document.write( "n = 171 - 130
\n" ); document.write( "n = 41
\n" ); document.write( ":
\n" ); document.write( "I get 342 pennies, 41 nickels, 96 dimes, 34 quarters\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check this, find the weight of each type of coin plus weight of the jar:
\n" ); document.write( "342(2.5) + 41(5) + 96(2.3) + 34(5.8) + 301 = 1779
\n" ); document.write( ":
\n" ); document.write( "-----------------------
\n" ); document.write( "Actually there is another solution to the problem which you can confirm
\n" ); document.write( "342 pennies, 76 nickels, 88 dimes, 7 quarters
\n" ); document.write( ":
\n" ); document.write( "We had to resort to finding integers from the Ti83 equation, because we had 4 unknowns and only 3 equations. \n" ); document.write( "

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