there the problemis in description

Question

This a word problem which requires systems of equations. Please show all work and you do not need to graph.        2 students are going to the store to buy supplies. one of them buys 2 packs of pencils and 3 packs of pens for $8.25.The other buys 5 packs of pencils and 2 packs of pens for $11. Find the cost of 1 pack of pencils and 1 pack of pens.                                                                              

Answer 1

use the addition method.

let x= the cost of one pack of pencils; let y=cost of one pack of pens.

 

so,

 

2x+3y=825

5x+2y=11

 

multiply the 2nd equation by -1 (multiplication property), we want to isolate one of the variables.

 

(5x+2y=11)(-1)

-5x -2y= - 11

now add both equations:

 

2x+3y=825

-5x-2y= - 11

--------------------

- 3x + y = 814 (y variable is now by itself, next solve for Y)

y=3x + 814

 

next. plug the value of y in equation #1

 

2x+3(3x+814)=825

2x+9x+2442=825

11x=825-2442

 

x= - 1617/11 

 

x= - 147

 

Now plug the value of x in equation #2 to find the new value of Y

 

5(-147)+2y=11

- 735 + 2y = 11

2y= 11+ 735

 

y= 746/2

 

y= 373   or $ 3.73 (value of 2 packs of pens)

 

proof: use either equation (2nd equation was used)

5(- 147) +2(373)= 11

 

now reasoning: subtract from the total value, the value of the pens.

$11.00 - $ 3.73 = 727 or $ 7.27 (5 packs of pencils)

 

$7.27 / 5 = $ 1.45 (cost of one pack of pencils)

 

$ 3.73 / 2 = $ 1.865 (cost of one pack of pens)

 

 

 

 

Answer 2

Use c for pencils and p for pens.

 

The two equations are as follows:

 

2c+3p=8.25

5c+2p=11

 

Now use elimination to solve for c & p.

 

Cancel out the p's by multiplying 2 by the top equation and -3 by the bottom equation.

2(2c+3p=8.25) = 4c+6p=16.5

-3(5c+2p=11)  = -15c-6p=-33

 

Now add the two equations together (combine like terms).

4c+6p=16.5

-15c-6p=-33

____________

-11c+0=-16.5

-11c=-16.5  (divide both sides by -11)

c=1.5 or $1.50 cost of pencils

 

Now find p by plugging c=1.5 into one of the original equations

2c+3p=8.25

2(1.5)+3p=8.25

3+3p=8.25  (subtract 3 from both sides)

3p=5.25    (divide both sides by 3)

p=1.75 or $1.75 cost of pens

 

Have a great day!!

Tiffany