Margie has 5 times as many nickels as quarters. She has a total of $2.00.
a. Write a system of equations to represent the situation. Let n represent
the number of nickels and q represent the number of quarters.
b. Solve the system you wrote in part (a). Show your work.
c. Interpret your solution in the context of the problem.
Please help
a. n = 5 q
... 5n + 25 q = 200
a. To represent the given situation with a system of equations:
1) The total number of nickels, n, is five times the total number of quarters, q: n = 5q.
2) The total value of the nickels (in cents) is 5n, and the total value of the quarters is 25q. We can convert these amounts to dollars and add them up: 0.05n + 0.25q = 2.00.
b. To solve the system of equations:
Substitute n = 5q from equation (1) into equation (2):
0.05(5q) + 0.25q = 2.00
0.25q + 0.25q = 2.00
0.50q = 2.00
q = 2.00 / 0.50
q = 4
Now substitute q = 4 into equation (1):
n = 5(4)
n = 20
So, there are 4 quarters (q = 4) and 20 nickels (n = 20).
c. The solution to the system of equations is q = 4 and n = 20. This means that Margie has 4 quarters and 20 nickels.
a. To represent the situation described, we can create two equations based on the given information:
1. "Margie has 5 times as many nickels as quarters":
n = 5q
2. "She has a total of $2.00":
0.05n + 0.25q = 2.00
In the first equation, n represents the number of nickels and q represents the number of quarters. The equation states that the number of nickels is 5 times the number of quarters.
In the second equation, 0.05 represents the value of a nickel in dollars and 0.25 represents the value of a quarter in dollars. The equation states that the total value of nickels (0.05n) plus the total value of quarters (0.25q) is equal to $2.00.
b. To solve the system of equations, we can use substitution or elimination.
Substituting the value of n from the first equation into the second equation, we have:
0.05(5q) + 0.25q = 2.00
0.25q + 0.25q = 2.00
0.50q = 2.00
q = 2.00 / 0.50
q = 4
Now, substituting the value of q into the first equation, we can find n:
n = 5(4)
n = 20
Therefore, the solution to the system of equations is n = 20 and q = 4.
c. The solution to the system of equations indicates that Margie has 20 nickels and 4 quarters. This means she has 5 times as many nickels as quarters. The total value of the nickels is 20 * $0.05 = $1.00, and the total value of the quarters is 4 * $0.25 = $1.00. Therefore, the total value of all the coins is $2.00, which matches the given information.