Lucy has 38 coins consisting of nickels and quarters amounting to $5.10. How many coins of each kind does she have

Question

how many nickels and quarters does she have

Answer 1

This is a system of equations:

 

q + n = 38 coins

 

25q + 5n = 510, which is the combined value of the coins (expressed as cents, so we don't have to deal with decimals.)

 

Solve the system by eliminating one of the variables, which you can do by multiplying the first equation by 5 and subtracting it from the second one:

 

     25q  +  5n = 510

   -   5q  + 5n = 190

_________________

      20q         = 320

 

q = 16

 

So there are 16 quarters, equaling 400 cents (4 dollars), and therefore 22 nickels equaling 110 cents ($1.10)

 

Together they make 510 cents, or $5.10

 

:-)