John and harry went to a stationery shop. john bought 3 pens and 8 notebooks for $20.50. harry bought 4 pens and 5 notebooks for $16.00. identify the cost of a pen and the cost of a notebook. asap!

1) 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

Again:

cost of notepads*number of notepads + cost of pens*number of pens = total cost

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 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

2) 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 is $24

1 pencil is $2.40

Total= $36

9 pens = 36

Therefore 1 pen is $4 BRANLIST PLEASE FOR MY VIRUTOS ANSWER

the least common denominator is 40

fwms@lil_ben06

step-by-step explanation: