Question

Rachel has 20 nickels, dimes, and quarters worth $3.70. if she has twice as many quarters as dimes, how many nickels does she have?

Answer 1

Answer: 2 nickels

Rachel has 20 coins composed of nickles, dimes and quarters amounting to $3.70. Her quarters are twice the number of her dimes, the number of nickels can be computed as follows:

If  X= the number of dimes  at .10 each

Then  2x= the number of quarters at .25 each and

20-(X-2X)= the number of nickels at .05 each

The equation will be: X(.1)+2(X).25+(20-X-2X).10=3.70 .1X+2X(.25)+(20-X-2X).05=3.70 .1X+.5X+(20-3X).05=3.70 .6X+(1-.15X)=3.70 .6X+1-.15X=3.70 .45X=3.70-1 .45X=2.70 X=2.70/.45 X=6 number of dimes 2X=12 number of quarters 20-6-12=2 number of nickels