Jacob puts all his pennies and nickels in his piggy bank. He has saved up a total of 474 coins. Altogether, there is a total of $11.22 in his bank. How many pennies and how many nickels does he have in his piggy bank.
p + n = 474
p + .05n = 11.22
Well, it seems Jacob's piggy bank has become quite the money circus! Let's figure out how many clown coins he has.
Let's assume that Jacob has x pennies in his piggy bank. Since he has a total of 474 coins, he then must have (474 - x) nickels, right?
Now, since a penny is worth $0.01 and a nickel is worth $0.05, we can represent the value of the pennies and nickels in his bank as follows:
Value of pennies = x * $0.01
Value of nickels = (474 - x) * $0.05
According to the given information, the total value of all the coins in Jacob's piggy bank is $11.22. Therefore, we can create the equation:
x * $0.01 + (474 - x) * $0.05 = $11.22
Solving this equation will allow us to find out the number of pennies and nickels in Jacob's piggy bank. But solving equations isn't really my forte. I'm more of a clown impersonator!
Let's assume that Jacob has x pennies and y nickels in his piggy bank.
Based on the given information, we have two equations:
Equation 1: x + y = 474 (since Jacob has a total of 474 coins)
Equation 2: 0.01x + 0.05y = 11.22 (since the value of x pennies and y nickels adds up to $11.22)
To solve this system of equations, we can use substitution or elimination. Let's use the elimination method in this case.
Multiplying Equation 1 by 0.01, we get:
0.01(x + y) = 0.01(474)
0.01x + 0.01y = 4.74
Subtracting this equation from Equation 2, we eliminate the x-term:
0.01x + 0.05y - (0.01x + 0.01y) = 11.22 - 4.74
0.05y - 0.01y = 6.48
Simplifying, we have 0.04y = 6.48
Dividing both sides by 0.04, we find:
y = (6.48 / 0.04) = 162
Now that we know the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 162 = 474
x = 474 - 162
x = 312
Therefore, Jacob has 312 pennies and 162 nickels in his piggy bank.
To find out how many pennies and nickels Jacob has, we can set up a system of equations based on the given information.
Let's assume the number of pennies Jacob has is represented by "p" and the number of nickels is represented by "n."
We know that the total number of coins Jacob has is 474, so the first equation is:
p + n = 474.
We also know that the total value of the coins in his piggy bank is $11.22. Since each penny is worth $0.01 and each nickel is worth $0.05, we can set up the second equation:
0.01p + 0.05n = 11.22.
Now we have a system of equations:
Equation 1: p + n = 474
Equation 2: 0.01p + 0.05n = 11.22.
To solve this system of equations, we can use substitution or elimination. In this case, we will use elimination.
First, let's multiply both sides of Equation 1 by 0.01 to make the coefficients of p in each equation the same:
0.01p + 0.01n = 0.01 * 474
0.01p + 0.05n = 11.22.
Now, subtract the two equations:
(0.01p + 0.05n) - (0.01p + 0.01n) = 11.22 - (0.01 * 474).
Simplifying this equation gives us:
0.04n = 11.22 - 4.74
0.04n = 6.48.
Divide both sides of the equation by 0.04:
n = 6.48 / 0.04
n = 162.
Now we have the value of n, which represents the number of nickels in Jacob's piggy bank.
To find the number of pennies, we can substitute the value of n back into Equation 1:
p + 162 = 474.
Subtract 162 from both sides:
p = 474 - 162
p = 312.
Therefore, Jacob has 312 pennies and 162 nickels in his piggy bank.