A purse contains 58 coins consisting of dimes and nickels. If the total amount of these coins amounted to $4.80, how many dimes and nickels are in the purse?
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 58-x.
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
NICKELS x $0.05 $0.05x
DIMES 58-x $0.10 $0.10(56-x)
-------------------------------------------
TOTALS 58 ----- $4.80
The equation comes from the column on the right
0.05x + 0.10(58-x) = 4.80
Get rid of decimals by multiplying every term by 100
5x + 10(58-x) = 480
5x + 580 - 10x = 480
-5x + 580 = 480
-5x = -100
x = 20 = the number of nickels
The number of dimes is 58-x or 58-20 or 38 dimes.
Checking: 20 nickels is $1.00 and 38 dimes is $3.80
And indeed $1.00+$3.80 = $4.80.
Edwin