In one shop price of pens and pencils are different.Two pencils and three pens cost 78$.three pencils and two pens cost 72$.what is the price of one pencil

Question

What will be the ans step by step

Answer 1

Let's say that the cost of pens = x

and the cost of pencils = y

 

Then we can set up a system of linear equations

 

2y + 3x = 78

3y + 2x = 72

 

Now, let's multiply the top equation by 3 and the bottom equation by 2. After that, we will subtract the two

 

6y + 9x= 234

6y + 4x = 144

 

Subtracting gives us 

 

5x = 90

 

x = 18

 

Now plug x = 18 into either of the two above equations. Let's choose the first equation

 

2y + 3x = 78

2y + 3(18) = 78

2y + 54 = 78

2y = 78 - 54

2y = 24

y = 12

 

Pens are $18 each and pencils are $12 each (are you sure that it isn't cents rather than dollars?)

Answer 2

Ishfaq, we need a system of equations. Let's let c = the number of pencils and n = the number of pens.

 

These are expensive pens and pencils, but I'll use your numbers.

 

2c + 3n = 78

3c + 2n = 72

 

This looks like we should use elimination. To make the c's match up, let's multiply the 1st equation by -3 and the 2nd by 2. Then we have...

 

-6c - 9n = -234

 6c + 4n = 144

 

Adding these together, we get...

 

-5n = -90

   n = 18

 

Then, we substitute...

 

2c + 3(18) = 78

     2c + 54 = 78

              2c = 24

                 c = 12

 

Each pencil costs $12 and each pen costs $18.