In his pocket Sam had $4 composed solely of quarters and nickels. He had a total of 20 coins. How many nickels did he have?
5 n + 25 q = 400 cents
n + q = 20
5 n + 25 q = 400 cents
5 n + 5 q = 100
------------------------------- subtract
20 q = 300
etc
Well, it seems like Sam had a pocket full of change! If he had a total of 20 coins and only quarters and nickels, we can set up an equation. Let's call the number of quarters "q" and the number of nickels "n."
We know that the total number of coins is 20, so we can write the equation: q + n = 20.
We also know that the total value of the coins in his pocket is $4, and since each quarter is worth $0.25 and each nickel is worth $0.05, we can write another equation: 0.25q + 0.05n = 4.
Now, let's solve this clownishly fun puzzle! By using some mathematical magic, we can multiply the second equation by 100 to eliminate the decimals. This gives us: 25q + 5n = 400.
Next, let's multiply the first equation by 5 to make it easier to eliminate one variable. We have: 5q + 5n = 100.
Now, if we subtract the second equation from the first equation, we'll be left with: (25q + 5n) - (5q + 5n) = 400 - 100.
This simplifies to: 20q = 300.
And finally, by dividing both sides of the equation by 20, we find that q (the number of quarters) is equal to 15.
Since Sam had a total of 20 coins, and we know he had 15 quarters, we can subtract 15 from 20 to find the number of nickels: 20 - 15 = 5.
So, Sam had 5 nickels in his pocket! It looks like he was quite the coin collector, or maybe he just really needed change for the snack machine.
To solve this problem, we can use a system of equations. Let's assign variables to represent the number of quarters and nickels Sam had.
Let's say the number of quarters Sam had was "q" and the number of nickels he had was "n".
We know that Sam had a total of 20 coins, so we can write the equation:
q + n = 20 (Equation 1)
We also know that the value of the coins in his pocket was $4. Since a quarter is worth $0.25 and a nickel is worth $0.05, we can write another equation to represent the value of the coins:
0.25q + 0.05n = 4 (Equation 2)
Now we can solve this system of equations to find the values of q and n.
Let's multiply Equation 1 by 0.05 to make the coefficients of n in both equations the same:
0.05q + 0.05n = 1 (Equation 3)
Now, let's subtract Equation 3 from Equation 2 to eliminate n:
(0.25q + 0.05n) - (0.05q + 0.05n) = 4 - 1
0.25q - 0.05q = 3
0.20q = 3
Now divide both sides of the equation by 0.20:
q = 3 / 0.20
q = 15
Now that we know q = 15, we can substitute this value back into Equation 1 to find n:
15 + n = 20
n = 20 - 15
n = 5
Therefore, Sam had 5 nickels.
To solve this problem, you can set up a system of equations. Let's use the variables q for the number of quarters and n for the number of nickels.
We know that the total value of the coins Sam had is $4, so we can write the equation:
0.25q + 0.05n = 4
We also know that the total number of coins is 20, so we can write the equation:
q + n = 20
To solve the system of equations, we can use substitution or elimination. Let's use substitution in this case.
First, isolate one of the variables in the second equation. Subtract q from both sides:
n = 20 - q
Now substitute this expression for n in the first equation:
0.25q + 0.05(20 - q) = 4
Simplify the equation:
0.25q + 1 - 0.05q = 4
0.2q + 1 = 4
0.2q = 3
Divide both sides by 0.2 to solve for q:
q = 3 / 0.2
q = 15
So, Sam had 15 quarters.
To find the number of nickels, substitute the value of q back into either equation:
n = 20 - q
n = 20 - 15
n = 5
Therefore, Sam had 5 nickels.