Question 215524
Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have?


Step 1.  Let x be the number of quarters and 0.25x dollar value of x quarters.


Step 2.  Let 2x be the number of dimes and 0.10*2x=.20x dollar value of 2x dimes.


Step 3.  Let x+9 be the number of nickels and .05(x+9)=0.05x+0.45 dollar value of x+9 nickels.


Step 4.  Then,  total value is 0.25x+0.20x+0.05x+0.45=2.45.  Solving yields the following steps.


*[invoke explain_simplification "0.25x+0.20x+0.05x+0.45=2.45" ]


With x=4 , then 2x=8    and x+9=13


Check total...4*0.25+8*0.10+13*.05=1.00+0.80+0.65=2.45 which is a true statement.


Step 5.  The number of quarters is 4 , the number of dimes is 8 , and the number of nickels is 13 .


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J