The 13 Coins

    2) Suppose a person had 13 coins (quarters and dimes) that equal
$2.05.  How many of each coin does that person have?
 
    25x + 10(13 - x) = 205
 
    25x + 130 -10x = 205
 
    15x + 130 = 205
    
    15x = 75
 
    x = 5
 
    Since "x" stands for the quarters, and there are 5, then we
know that there are 8 dimes.  Of course, this can also be seen
in the term for the dimes -- "10(13-x)."   Since "x" = "5," then
13-5 = 8 (for the number of dimes), and multiplying by 10 gives
us the value of 80 cents.  To double check,  make sure that the
right  sum was obtained with the right number of coins.