A jar contains n nickels and d dimes. There are 22 coins in the jar, and the total value of the coins is $1.60. How many nickels and how many dimes are in the jar?
Let n be the number of nickels in the jar and let d be the number of dimes.
There are 22 coins in the jar, so we can make this equation:
n + d = 22 Let's subtract d from both sides of this equation
n = 22 - d
The total value of the coins is $1.60, so we can make this equation:
0.05n + 0.10d = 1.60
We can multiply both sides of the equation through by 10
5n + 10d = 160
Since n = 22 - d we can substitute 22 - d in for n
5(22 - d) + 10d = 160
Distribute 5 to each term in parenthesees
110 - 5d + 10d = 160
Combine -5d and 10d to get 5d
110 + 5d = 160
Subtract 110 from both sides of the equation
5d = 50
Divide both sides of the equation by 5
d = 10
Now that we know d = 10 we can find n by substituting 1 for d in the first equation.
n = 22 - d = 22 - 10 = 12
So there are 12 nickels and 10 dimes.