At an office supply store, Samantha bought 5 notebooks and 2 pens for $9. Jeffrey bought 3 notebooks and 2 pens for $6. Find the price of a notebook and the price of a pen.
(please help I'm stuck)
5 n + 2 p = 9
3 n + 2 p = 6
subtract the equations to eliminate p ... 2 n = 3
... solve for n, then substitute back to find p
To find the price of a notebook and the price of a pen, we can set up a system of equations based on the given information.
Let's assume the price of a notebook is "x" dollars, and the price of a pen is "y" dollars.
From the first statement, "Samantha bought 5 notebooks and 2 pens for $9," we can translate this into an equation:
5x + 2y = 9. This equation represents Samantha's purchase.
Similarly, from the second statement, "Jeffrey bought 3 notebooks and 2 pens for $6," we can translate this into another equation:
3x + 2y = 6. This equation represents Jeffrey's purchase.
Now, we have a system of equations:
5x + 2y = 9
3x + 2y = 6
We can solve this system of equations using the method of elimination:
First, subtract the second equation from the first equation to eliminate the "y" variable:
(5x + 2y) - (3x + 2y) = 9 - 6
5x - 3x + 2y - 2y = 3
2x = 3
x = 3/2
x = 1.5
Now that we have found the value of "x," which represents the price of a notebook, we can substitute it back into one of the original equations to find the value of "y":
Using the first equation:
5(1.5) + 2y = 9
7.5 + 2y = 9
2y = 9 - 7.5
2y = 1.5
y = 1.5/2
y = 0.75
Therefore, the price of a notebook is $1.50, and the price of a pen is $0.75.