a college student only saves quarters and dimes in her piggy bank. she empties out her piggy bank at the end of each month. this month there are 28 quarters and dimes. the total value of the coins is $4.05. how many quarters and dimes does the college student have?

For this case, the first thing we must do is define variables:
 x = number of quarters
 y = number of dimes
 We now write the system of equations:
 x + y = 28
 0.25x + 0.10y = 4.05
 Solving the system of equations we have:
 x = 8.33
 y = 19.66
 Rounding:
 x = 8
 y = 20
 
 the college student has:
 8 quarters
 20 dimes