Answer:
n + d = 60
0.05n + 0.1d = 4.45
The jar contains: 31 nickels and 29 dimes.
Explanation:
Numbers of coins: n nickels and d dimes
Total number of coins: n + d
Total number of coins: 60
Equation 1: n + d = 60
Values of the coins:
n nickels are worth 0.05n
d dimes are worth 0.1d
Total value of all coins: 0.05n + 0.1d
Total value of coins: $4.45
Equation 2: 0.05n + 0.1d = 4.45
System of equations:
n + d = 60
0.05n + 0.1d = 4.45
Solve the first equation for n.
n = 60 - d
Substitute 60 - d for n in the second equation.
0.05n + 0.1d = 4.45
0.05(60 - d) + 0.1d = 4.45
3 - 0.05d + 0.1d = 4.45
3 + 0.05d = 4.45
0.05d = 1.45
d = 29
There are 29 dimes.
n + d = 60
n + 29 = 60
n = 31
There are 31 nickels.
The jar contains:
31 nickels and
29 dimes.