Question 221479
Suppose you have a coin collection of dimes and quarters containing 46 coins. if you have $6.70, how many of each type of coin do you have?


Step 1.  Let x be the number of dimes.


Step 2.  Let 0.10x be the dollar value of dimes


Step 3.  Let 46-x be the number of quarters


Step 4.  Let 0.25(46-x) be the dollar value of quarters.


Step 5.  Then  0.10x+0.25(46-x)=6.70 be the total dollar value of dimes and quarters.


Step 6.  The following steps will solve the equation in Step 5.


*[invoke explain_simplification "0.10x+0.25(46-x)=6.70" ]


With x=32, then 46-x=14.  Check dollar value in Step 5.  


0.10*32+0.25*14=3.20+3.50=6.70 which is a true statement.


Step 7.  ANSWER:  The number of dimes is 32 and the number of quarters is 14.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J