Question 223797
A mixture of dimes and quarters has a total value of $10.20. There are 57 coins in all. How many of each type are present?


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=10.20 be the total dollar value.


Step 6.  Also, x+y=57  since there are 57 coins


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


{{{0.25x+0.10y=10.20}}}
{{{x+y=57}}}


*[invoke linear_substitution "x", "y", 0.25, 0.10, 10.20, 1, 1, 57 ]


So x=30 and y=27.  The difference is 3 and the total dollar value is 0.25*30+0.10*27=7.50+2.70=10.20 which is a true statement.  And the total number of coins is 57.


Step 8.  ANSWER:  The number of quarters is 30 and the number of dimes is 27.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J