Use a system of equations to solve problem
Emily emptied her bank ana totaled the nickels, dimes, and quarters that she had saved. The total amount was 14.50
The number of dimes was 2 more than 3 times the number of nickels. How many of each coin were there
Can you show the steps i just cant do this can you show every step so i can understand this please help me out
Have some patience. See your first post.
"I need HELP!!" is a strange name for a school subject.
I'm sorry, but we don't have any experts in that subject.
Of course! I'll break down the steps for you to solve this problem using a system of equations.
Let's start by defining our variables:
Let's say the number of nickels is represented by "N".
The number of dimes is 2 more than 3 times the number of nickels, which can be represented by "3N + 2".
Lastly, let's say the number of quarters is represented by "Q".
Now, let's set up the system of equations using the given information:
1. The total value of all the coins is $14.50:
0.05N + 0.10(3N + 2) + 0.25Q = 14.50
2. The number of dimes is 2 more than 3 times the number of nickels:
3N + 2 = D
Now, we have a system of two equations:
Equation 1: 0.05N + 0.10(3N + 2) + 0.25Q = 14.50
Equation 2: 3N + 2 = D
To solve this system of equations, we'll use the substitution method:
Step 1: Substitute the value of "D" from Equation 2 into Equation 1:
0.05N + 0.10(3N + 2) + 0.25Q = 14.50
0.05N + 0.30N + 0.20 + 0.25Q = 14.50
0.35N + 0.25Q = 14.30 (simplified equation)
Step 2: Solve Equation 2 for "D":
D = 3N + 2
Step 3: Substitute the value of "D" from Equation 2 back into the simplified Equation 1:
0.35N + 0.25Q = 14.30
Now, we have a system with two variables:
Equation 1: 0.35N + 0.25Q = 14.30
Equation 2: D = 3N + 2
To solve this system, we need another equation. Let's use the information about the total number of coins:
Step 4: Create a third equation based on the total number of coins:
N + D + Q = total number of coins
Now, substitute the value of "D" from Equation 2 into the third equation:
N + (3N + 2) + Q = total number of coins
4N + 2 + Q = total number of coins
At this point, we have a system of three equations:
Equation 1: 0.35N + 0.25Q = 14.30
Equation 2: D = 3N + 2
Equation 3: 4N + 2 + Q = total number of coins
Solving this system of equations will give us the values of "N," "D," and "Q," which represent the number of nickels, dimes, and quarters, respectively.
You can use any preferred method to solve this system, such as substitution or elimination. Once you find the values of "N," "D," and "Q," you will have the solution to the problem.