Snooki has a total of 25 quarters and pennies in her pocket. She has $2.32 altogether. How many quarters and pennies were sold?
25 q + p = 232
q + p = 25
Need I go on?
Yes
To find the number of quarters and pennies Snooki has, we can set up a system of equations. Let's use the variable "q" to represent the number of quarters and "p" to represent the number of pennies.
1. The first equation represents the total number of coins: q + p = 25
Since Snooki has a total of 25 quarters and pennies in her pocket.
2. The second equation represents the total value of the coins: 0.25q + 0.01p = 2.32
Since each quarter is worth 0.25 dollars and each penny is worth 0.01 dollars, and the total value of the coins is $2.32.
To solve the system of equations, we can use substitution, elimination, or any other method. For this example, let's use the substitution method.
From the first equation, we can express p in terms of q by subtracting q from both sides of the equation:
p = 25 - q
Now, substitute this expression for p in the second equation:
0.25q + 0.01(25 - q) = 2.32
Simplify the equation:
0.25q + 0.25 - 0.01q = 2.32
Combine like terms:
0.24q + 0.25 = 2.32
Subtract 0.25 from both sides:
0.24q = 2.32 - 0.25
0.24q = 2.07
Divide both sides by 0.24:
q = 2.07 / 0.24
q ≈ 8.625
Since the number of quarters must be a whole number, we can approximate q to the nearest whole number:
q = 9
Now substitute this value back into the first equation to find p:
9 + p = 25
p = 25 - 9
p = 16
Therefore, Snooki has 9 quarters and 16 pennies in her pocket.