Question 45161
lets say the the nickels is n while the dimes is d.



first equation


n + d = the number of coins


n + d = 50



second equation


amount of a nickel ( n ) + amount of a dime ( d ) = the total amount


0.05 ( n ) + 0.10 ( d ) = $3.50


multiply to both side by 100 beacause we need to make the dollar to cent so if 


you convert $1=100 cents.


100 [ 0.05 ( n ) + 0.10 ( d ) = $3.50 ] 100


5 ( n ) + 10 ( d ) = 350


5n + 10d = 350


so the second equation is 5n + 10d = 350


Now, we solve the two equations to get the no. of dimes:


 n +   d =  50

5n + 10d = 350


Then, we multiply the first equation by -5. The result would be like this:


-5n -  5d = -250
 5n + 10d =  350

5d = 100


then, divide both side by the numerical co-efficient 5 .

d = 20

so, the number of dimes is 20.


now, the no. of nickels: 


now, we have to substitute d to 20 and use equation 1(but you can use 

equation 2 if you like) because we can get the number of nickels.


n + 20 = 50


then, transpose 20 to the other side.


n = 30

so, the no. of nickels is 30.


THEN, WE CAN CONCLUDE THAT THE NO> OF DIMES IS 20 AND THE NICKEL IS 30.