Question

A jar containing only nickels (n) and dimes (d) contains a total of 60 coins. The value of all the coins in the jar is $4.45.

Write and solve a system of equations to find the amount of nickels and dimes that are in the jar.
Equation 1:
Equation 2:
The jar contains:
nickels and
dimes.
Blank 1:
Blank 2:
Blank 3:
Blank 4:

Answer 1

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.