Question 228903
A person has five times as many nickels as dimes. If the total face value of these coins is $4.90, how many of each type of coin does this person have? 


Step 1.  Let x be the number of dimes.


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


Step 3.  Let 5x be the number of nickels.


Step 4.  Let 0.05*5x=0.25x be the dollar value of nickels and since there are 5 times as many nickels as dimes.


Step 5.  Then, 0.10x+.25x=4.90 be the total dollar value.


Step 6.  Solving {{{0.10x+0.25x=4.90}}} yields the following steps:


{{{0.35x=4.90}}}


Divide 0.35 to both sides of the equation


{{{0.35x/0.35=4.90/0.35}}}


{{{x=14}}} and {{{5x=70}}}


Check the dollar value using the above numbers:


{{{0.10*14+0.05*70=1.40+3.50=4.90}}} which is a true statement.


Step 7.  ANSWER:  The number of dimes is 14 and the number of nickels is 70.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J