a piggy bank contains only quarters and nickels, and there is a total of 60 coins. The total value of the coins in the bank is 7.40 How many quarters are in the bank?
+3454 To solve this, we need to set up two equations and solve them like you would solving inequalities by elimination.
N + Q = 60 ---This one is telling us that 60 coins are made up of nickles and quarters.
.05N+.25Q = 7.40 ---This one is telling us that the total balance is $7.40 and quarters are worth 25 cents, and nickles are worth 5 cents.
If we move the decimal place over on all three numbers, we can write the second equation as:
5N+25Q=740
Now, to solve with elimination we need to have 5N in both the equations. Let's multiply everything in the first equation by 5 so we have 5N in both equations.
5(N + Q = 60)
5N+5Q=300
Now, we solve by elimination with our two new equations.
5N+25Q=740
-5N -5Q= -300
20Q=440
Q = 22 ---Divide both sides by 20
There are twenty-two quarters!
To find how many nickles there are, put in 22 instead of Q for one of the equations (we can do this because Q = 22)
Let's take our original first equation.
N + Q = 60
N + 22 = 60
N = 38 ---Subtract 22 from both sides
There are 38 nickles!
To check this, let's put in these values of N and Q into our original second equation.
.05N+.25Q = 7.40
.05(38)+.25(22) = 7.40
1.9+5.5 = 7.40
7.4 = 7.4
It works!
+3454 To solve this, we need to set up two equations and solve them like you would solving inequalities by elimination.
N + Q = 60 ---This one is telling us that 60 coins are made up of nickles and quarters.
.05N+.25Q = 7.40 ---This one is telling us that the total balance is $7.40 and quarters are worth 25 cents, and nickles are worth 5 cents.
If we move the decimal place over on all three numbers, we can write the second equation as:
5N+25Q=740
Now, to solve with elimination we need to have 5N in both the equations. Let's multiply everything in the first equation by 5 so we have 5N in both equations.
5(N + Q = 60)
5N+5Q=300
Now, we solve by elimination with our two new equations.
5N+25Q=740
-5N -5Q= -300
20Q=440
Q = 22 ---Divide both sides by 20
There are twenty-two quarters!
To find how many nickles there are, put in 22 instead of Q for one of the equations (we can do this because Q = 22)
Let's take our original first equation.
N + Q = 60
N + 22 = 60
N = 38 ---Subtract 22 from both sides
There are 38 nickles!
To check this, let's put in these values of N and Q into our original second equation.
.05N+.25Q = 7.40
.05(38)+.25(22) = 7.40
1.9+5.5 = 7.40
7.4 = 7.4
It works!
