There are 25 coins inside a container. Some of the coins are nickels, and the rest are quarters. The value of the coins is $4.05. Let n represent the number of nickels, and let q represent the number of quarters. Which system of equations represents this situation?
surely the correct choice will look something like
n+q = 25
5n+25q = 405
"Which system … ?"
Are there supposed to be choices??
why though?
To solve this problem and determine the system of equations that represents the situation, we need to use the information provided.
Let's break down the given information:
1. There are 25 coins in total.
2. Some coins are nickels, and the rest are quarters.
3. The value of all the coins is $4.05.
To represent this situation mathematically, we need to define two variables: n for the number of nickels and q for the number of quarters.
1. The equation that represents the total number of coins can be written as:
n + q = 25
Since there are 25 coins in total, the sum of the nickels (n) and quarters (q) should equal 25.
2. The equation that represents the total value of the coins can be written as:
0.05n + 0.25q = 4.05
This equation represents the value of the coins. The value of a nickel (n) is $0.05, and the value of a quarter (q) is $0.25. The sum of the values of the nickels and quarters should equal the total value of $4.05.
Therefore, the system of equations that represents this situation is:
n + q = 25
0.05n + 0.25q = 4.05