Question 1020549: Jane had 12 coins in her purse that have a total of $1. If these coins consist of nickels and dimes, how many of each does she have? Answer by Edwin McCravy(20060) (Show Source):
Let the number of nickels be x
Let the number of dimes be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
nickels x $0.05 $0.05x
dimes y $0.10 $0.10y
-------------------------------------------
TOTALS 12 ----- $1.00
The first equation comes from the second column.
x + y = 12
The second equation comes from the last column.
0.05x + 0.10y = 1
Get rid of decimals by multiplying every term by 100:
5x + 10y = 100
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 12
y = 12 - x
Substitute (12 - x) for y in 5x + 10y = 100
5x + 10(12 - x) = 100
5x + 120 - 10x = 100
-5x + 120 = 100
-5x = -20
x = 4 = the number of nickels.
Substitute in y = 12 - x
y = 12 - (4)
y = 8 dimes.
Checking: 4 nickels is $0.20 and 8 dimes is $0.80
That's 12 coins.
And indeed $0.20 + $0.80 = $1.00
Edwin
