Answer the following math questions

Question

1) Cynthia bought some 2 similar notepads and 3 similar pens for $40.30. Annie bought 3 of the same notepads and 5 of the same pens for $61. What was the cost for one notebook and one pen.

 

2) Ronda has some money . She can either buy 15 pencils or 9 pens with all her money. She buys 10 pencils for $24 and some pens. How much is one pen?

 

Answer 1

Hello Mohammad,

 

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

 

Answer:

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