Sarah has a collection of nickels, dimes, and pennies worth $5.06. She has five times as many nickels as pennies; and she has two times as many dimes as pennies. How many coins of each kind does she have?
The best way to even begin solving this problem, is to organize: N-Nickels P-Pennies D-Dimes N=0.05 P=0.01 D=0.10 Total= $5.06 We begin to write the equation as : 0.01p+0.05(5p)+0.10(2p)=$5.06 p represents pennies so the 5p represents the fact that nickels equals 5 times the amount of pennies and the 2p represents the fact that dimes equals 2 times the amount of pennies. Multiply to get rid of the parenthesis. 0.01p+0.25p+0.20p=$5.06 Add up all the numbers on the left side of the equal sign: 0.46p=$5.06 Divide both side by 0.46 to isolate p. p=11. Therefore there are 11 pennies. Nickels is 5 times the amount of pennies so: 5*11=55 nickels. Dimes is 2 times the amount of pennies so: 2*11=22 dimes. 55 nickels is equal to $2.75 22 dimes is equal to $2.20 11 pennies is equal to $0.11 Add them all up and you get $5.06.
