if 6 notebooks + 2 binders = 23.52
ans 3 notebooks + 4 binders = 25.53
how do I solve to find out what the notebooks and binders each cost?
6n + 2b = 23.52
3n + 4b = 25.53
multiply the 1st equation by 2 and you have
12n + 4b = 47.04
3n + 4b = 25.53
now subtract to get
9n = 21.51
n = 2.39
Now you can get b
8 more than a number p is 17
To solve for the cost of each notebook and binder, you can set up a system of equations based on the given information and then solve for the variables.
Let's assign variables to represent the cost of a notebook and a binder. Let's say "n" represents the cost of a notebook and "b" represents the cost of a binder.
Based on the given information, we can set up two equations:
Equation 1: 6n + 2b = 23.52
This equation represents the total cost of 6 notebooks and 2 binders, which is equal to $23.52.
Equation 2: 3n + 4b = 25.53
This equation represents the total cost of 3 notebooks and 4 binders, which is equal to $25.53.
Now, you have a system of equations with two unknowns (n and b) to solve:
6n + 2b = 23.52 ---(1)
3n + 4b = 25.53 ---(2)
There are several methods to solve this system of equations, such as substitution, elimination, or matrix methods. Let's use the substitution method in this case:
From Equation 1, isolate "n":
6n = 23.52 - 2b
n = (23.52 - 2b) / 6 ---(3)
Substitute Equation 3 into Equation 2:
3[(23.52 - 2b) / 6] + 4b = 25.53
Now, you can solve this equation to find the value of "b" (the cost of a binder). Once you have the value of "b," substitute it back into Equation 3 to find the value of "n" (the cost of a notebook).
Solving this equation might involve simplification and algebraic operations. After finding the values of "n" and "b," you will know the cost of each notebook and binder.