Question 223618
John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution


Step 1.  Let x be the number of quarters.


Step 2.  Let 0.25x be the dollar value of quarters.


Step 3.  Let y be the number of dimes.


Step 4.  Let 0.10y be the dollar value of dimes.


Step 5.  Then 0.25x+0.10y=2.05 be the total dollar value.


Step 6.  Also, y=x+3  since there are 3 more dimes than quarters


Step 7.  Our linear system of equation is given in Steps 4 and 5 shown below:


{{{0.25x+0.10y=2.05}}}
{{{-x+y=3}}}


*[invoke linear_substitution "x", "y", 0.25, 0.10, 2.05, -1, 1, 3 ]


So x=5 and y=8.  The difference is 3 and the total dollar value is 0.25*5+0.10*8=2.05 which is a true statement.


Step 8.  ANSWER:  The number of quarters is 5 and the number of dimes is 8.


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