Margie has 5 times as many nickels as quarters. She has a total of $2.00.
Write a system of equations to represent the situation. Let n represent the number of nickels and q represent the number of quarters.
count the coins and the money:
n = 5q
5n+25q = 200
Sure thing! Let's break it down.
We know that Margie has 5 times as many nickels as quarters. So, we can set up the equation n = 5q.
We're also given that the total value of all the coins is $2.00. Now, a nickel is worth $0.05 and a quarter is worth $0.25. We can set up another equation to represent this:
0.05n + 0.25q = 2.00
So, the system of equations representing the situation is:
n = 5q
0.05n + 0.25q = 2.00
Now let's hope those coins don't start telling jokes!
To represent the given situation with a system of equations, we need to consider the total number of nickels and quarters Margie has, as well as the total value of all the coins.
Let's start by representing the number of nickels and quarters:
Let n represent the number of nickels
Let q represent the number of quarters
Given that Margie has 5 times as many nickels as quarters, we can express this relationship as:
n = 5q ---(Equation 1)
Next, we can consider the total value of the coins. Since the value of a nickel is $0.05 and the value of a quarter is $0.25, we can create an equation representing the total value of all the coins Margie has:
0.05n + 0.25q = 2.00 ---(Equation 2)
So, the system of equations to represent the given situation are:
n = 5q
0.05n + 0.25q = 2.00
To write a system of equations to represent the situation, we need to use the information given in the problem.
Let n represent the number of nickels and q represent the number of quarters.
1. "Margie has 5 times as many nickels as quarters": This can be represented as n = 5q. Since she has 5 times as many nickels, the number of nickels (n) is equal to 5 times the number of quarters (q).
2. "She has a total of $2.00": We can express the total value in cents to make the equation easier. Since there are 5 cents in a nickel and 25 cents in a quarter, the total value equation can be written as:
5n + 25q = 200
Using the information above, the system of equations can be written as:
n = 5q
5n + 25q = 200
n = 5 q
0.05 n + 0.25 q = 2.00 ( which is 5 n + 25 q = 200 )