Anna has 19 coins, all nickels and dimes. the coins' total
value is $1.55. How many nickels and dimes does she have?
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 19-x.
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
NICKELS x $0.05 $0.05x
DIMES 19-x $0.10 $0.10(19-x)
-------------------------------------------
TOTALS 19 ----- $1.55
The equation comes from the column on the right
0.05x + 0.10(19-x) = 1.55
Get rid of decimals by multiplying every term by 100
5x + 10(19-x) = 155
5x + 190 - 10x = 155
-5x + 190 = 155
-5x = -35
x = 7 = the number of nickels
The number of dimes is 19-x or 19-7 or 12 dimes.
Checking: 7 nickels is $0.35 and 12 dimes is $1.20
That's 7+12=19 coins and indeed $0.35+$1.20 = $1.55.
Edwin