Sang-Jin has only quarters and nickels in her piggy bank. She has 66 coins in the bank with a value of $11.50.
How many quarters are in Sang-Jin’s piggy bank?
The AI continues its streak of wrong answers !!
let a human do it:
quarters--- x
nickels --- 66 - x
25x + 5(66-x) = 1150
25x + 330 - 5x = 1150
20x = 820
x = 41
so 41 quarters and 66-41 or 25 nickels
check:
25(41) + 5(25)
= 1025 + 125 = 1150
Let's assume the number of quarters in Sang-Jin's piggy bank is q, and the number of nickels is n.
We can set up two equations based on the given information:
1. q + n = 66 (the total number of coins is 66)
2. 0.25q + 0.05n = 11.50 (the total value of coins is $11.50)
To solve this system of equations, we can use substitution or elimination method. Let's start with the substitution method.
From equation 1, we can express n = 66 - q.
Substituting this into equation 2:
0.25q + 0.05(66 - q) = 11.50
0.25q + 3.3 - 0.05q = 11.50
0.20q + 3.3 = 11.50
0.20q = 11.50 - 3.3
0.20q = 8.2
Now, let's solve for q by dividing both sides of the equation by 0.20:
q = 8.2 / 0.20
q ≈ 41
So, there are approximately 41 quarters in Sang-Jin's piggy bank.
To find out the number of quarters in Sang-Jin's piggy bank, we need to set up a system of equations based on the given information. Let's denote the number of quarters as q and the number of nickels as n.
We know that Sang-Jin has a total of 66 coins in the bank, so the first equation we can form is:
q + n = 66 (Equation 1)
The value of all the coins in the bank is $11.50. Quarters have a value of $0.25 each and nickels have a value of $0.05 each. Therefore, the second equation can be written as:
0.25q + 0.05n = 11.50 (Equation 2)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method to solve for q.
Multiply both sides of Equation 1 by 0.05 to make the coefficients of n the same:
0.05q + 0.05n = 3.30 (Equation 3)
Subtract Equation 3 from Equation 2 to eliminate n:
0.25q + 0.05n - (0.05q + 0.05n) = 11.50 - 3.30
0.25q - 0.05q = 8.20
0.20q = 8.20
Divide both sides by 0.20 to isolate q:
q = 8.20 / 0.20
q ≈ 41
So, there are approximately 41 quarters in Sang-Jin's piggy bank.