Answer:
$4
Explanation:
We need to set up an algebraic expression to solve this problem:
Let n= cost of a notepad
Let p= cost of a pen
First set up an expression for Cynthia's purchase:
cost of notepads*number of notepads + cost of pens*number of pens = total cost
n*2 + p*3 = 40.30
Rewrite as:
2n + 3p = 40.30
Next, set up an expression for Annie's purchase:
Here we will be using the same variables
n*3 + p*5 = 61
Rewrite as:
3n + 5p =61
Now, set up a system of equations:
2n + 3p = 40.30
3n + 5p =61
A system of equations can be solved in several ways, here I will use the addition/elimination method
For this method one of the variables must be able to be eliminated
Step 1: Pick a variable to eliminate
Here I will eliminate n
Step 2: make the selected variables in the equations equal and opposite so that they cancel out when the equations are added together
(2n + 3p = 40.30)(-3)
(3n + 5p =61)(2)
-6n - 9p = -120.90
6n + 10p = 122
Step 3: add vertically
-6n - 9p = -120.90
6n + 10p = 122
p = 1.10
Step 4: Figure out the other variable by inputting the answer you just got back into the original equation
2n + 3(1.10) = 40.30
2n + 3.30 = 40.30
-3.30 37
2n = 37
/2 /2
n = 18.5
One notebook = $18.50
One pen= $1.10
18.50+1.10= $19.60
2nd step
We must first set up an algebraic expression
total=15 pencils
total=9 pens
The total amount is the price of one pencil*15
To figure out one pencil:
10 pencils are $24
1 pencil is $2.40
Total= $36
9 pens = 36
Therefore 1 pen is $4