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 45 ----- $3.65
The first equation comes from the "Number of coins" column.
x + y = 45
The second equation comes from the last column.
0.05x + 0.10y = 3.65
Get rid of decimals by multiplying every term by 100:
5x + 10y = 365
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 45
y = 45 - x
Substitute (45 - x) for y in 5x + 10y = 365
5x + 10(45 - x) = 365
5x + 450 - 10x = 365
-5x + 450 = 365
-5x = -85
x = 17 = the number of nickels.
Substitute in y = 45 - x
y = 45 - (17)
y = 28 dimes.
Checking: 17 nickels is $0.85 and 28 dimes is $2.80
That's 45 coins.
And indeed $0.85 + $2.80 = $3.65
Edwin
