I have a bunch of nickels and quarters worth $7.85 in my [pocket. How do I write a system of equation to solve and determine how many of each coin I have!!
5N + 25Q = 785
N + 5Q = 157
N = 157 - 5Q
Of course you cannot have a unique solution, since you don't have enough information to form a second equation.
But...
you said he has a bunch of nickels and quarters, so he has at least one of each
so let Q be a number form 1 to 25 to get different combinations
Q N ------ combination ----------- value
1 152 ---- 1 quarter + 152 nickels = $7.85
2 147 -----2 quarters + 147 nickels = $7.85
...
25 32 ----- 25 quarters + 32 nickels = $7.85
To solve this problem, you can set up a system of equations based on the given information. Let's assume you have x nickels and y quarters.
The first equation represents the total value of the coins:
0.05x + 0.25y = 7.85
The second equation represents the total number of coins:
x + y = ?
However, we still need to find the value of x + y to complete the second equation.
To do this, we can multiply the value of each nickel, which is $0.05, by the number of nickels (x) and multiply the value of each quarter, which is $0.25, by the number of quarters (y). Adding these two products together will give us the total value of all the coins:
0.05x + 0.25y = $7.85
Now, we need to solve the equation x + y = ? to find the value of x + y. Since we don't have this value yet, we'll have to use the information provided in the question.
The question stated that the total value of the coins is $7.85. To determine how many nickels and quarters you have, you need to write an equation with this information.
Let's rewrite the equation in terms of x and y:
0.05x + 0.25y = 7.85
Now, you can use the second given piece of information: you have a total of x nickels and y quarters. Therefore, the total count of coins is:
x + y = (total count of coins)
By combining this equation with the first equation, you can now solve this system of equations to determine the values of x and y.