Julie is going to the mall. She has 15 coins in her pocket that nadd up to $2.18. She has the same number of pennies as she does dimes. she has 5 more quarters than she has nickels. If she has 3 pennies, how many quarters, dimes and nickles does Julie have?
3 pennies
3 dimes
2.18 - 0.33 = 1.85
7 quarters = 1.75
2 nickels = 0.10
She has 7 quarters and 2 nickels.
She has 3 pennies and 3 dimes.
7 quarters and 2 nickels and 3 dimes
7 quarters 3 pennies 3 dimes and 2 nickels
7 quarters 3 dimes 2 nickels 3 pennies
To solve this problem, we can break it down into smaller steps:
Step 1: Converting amount to cents
We know that Julie has $2.18, which is equal to 218 cents. So, we'll work with cents to keep calculations consistent.
Step 2: Writing equations based on given information
Let's denote the following:
- Number of pennies = P
- Number of dimes = D
- Number of nickels = N
- Number of quarters = Q
Based on the given information, we can write the following equations:
Equation 1: P + D + N + Q = 15 (as Julie has 15 coins)
Equation 2: P = D (as she has the same number of pennies as dimes)
Equation 3: Q = N + 5 (as she has 5 more quarters than nickels)
Step 3: Substituting equations into each other:
We can substitute Equation 2 into Equation 1 to eliminate P:
D + D + N + Q = 15
2D + N + Q = 15 (Equation 4)
We can substitute Equation 3 into Equation 4 to eliminate Q:
2D + N + N + 5 = 15
2D + 2N + 5 = 15
2D + 2N = 15 - 5
2D + 2N = 10 (Equation 5)
Step 4: Solving the system of equations
We now have two equations - Equation 2 and Equation 5 - with two variables (D and N). We can solve them simultaneously.
Equation 2: P = D
Equation 5: 2D + 2N = 10
From Equation 2, we know that P = 3 (given). Substituting this into Equation 5 and solving for D and N:
2D + 2N = 10
2D + 2(D) = 10 (as P = D = 3)
4D + 2N = 10
4D + 2N = 10
4D + 2(3) = 10
4D + 6 = 10
4D = 10 - 6
4D = 4
D = 4/4
D = 1
Substituting the value of D back into Equation 2, we can find N:
P = D
3 = 1
Finally, let's substitute the values of D and N into Equation 3 to find Q:
Q = N + 5
Q = 1 + 5
Q = 6
So, Julie has 1 dime, 1 nickel, and 6 quarters.