document.write( "Question 176671This question is from textbook
\n" ); document.write( ": Sam found a number of nickels, dimes and quarters in his room. He found 3 more dimes than nickels but twice as many quarters as dimes. The total value of the coins was $5.05 how many coins of each type did Sam find? \n" ); document.write( "
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let n = number of nickels
\n" ); document.write( "let d = number of dimes
\n" ); document.write( "let q = number of quarters.
\n" ); document.write( "---
\n" ); document.write( "d = n+3
\n" ); document.write( "q = 2*d = 2*(n+3) = 2*n+6
\n" ); document.write( "---
\n" ); document.write( "since:
\n" ); document.write( "$5.05 * 100 = 505 cents
\n" ); document.write( "and:
\n" ); document.write( "5*n = number of nickels * 5 cents per nickel
\n" ); document.write( "10*d = number of dimes * 10 cents per dime
\n" ); document.write( "25*q = number of quarters * 25 cents per quarter
\n" ); document.write( "then:
\n" ); document.write( "5*n + 10*d + 25*q = 505 cents
\n" ); document.write( "---
\n" ); document.write( "since d = n+3,
\n" ); document.write( "and q = 2d = 2*n+6,
\n" ); document.write( "then:
\n" ); document.write( "5*n + 10*(n+3) + 25*(2*n+6) = 505
\n" ); document.write( "---
\n" ); document.write( "remove parentheses and this equation becomes:
\n" ); document.write( "5*n + 10*n + 30 + 50*n + 150 = 505
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "65*n + 180 = 505
\n" ); document.write( "subtract 180 from both sides to get:
\n" ); document.write( "65*n = 325
\n" ); document.write( "divide both sides by 65 to get:
\n" ); document.write( "n = 5
\n" ); document.write( "---
\n" ); document.write( "number of nickels = 5
\n" ); document.write( "number of dimes is number of nickels + 3 = 8
\n" ); document.write( "number of quarters is 2 times number of dimes = 16
\n" ); document.write( "---
\n" ); document.write( "5 nickels times 5 cents each is 25 cents
\n" ); document.write( "8 dimes times 10 cents each is 80 cents
\n" ); document.write( "16 quarters times 25 cents each is 400 cents
\n" ); document.write( "400 cents + 80 cents + 25 cents = 505 cents.
\n" ); document.write( "divide 505 cents by 100 to get:
\n" ); document.write( "$5.05
\n" ); document.write( "---
\n" ); document.write( "answer is:
\n" ); document.write( "sam found 5 nickels, 8 dimes, and 16 quarters.
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