Question

John bought some pens and pencils at book store. if 5 pens and 3 pencils cost $13 while 5 pencils and 3 pens cost $11 instead, find the cost of a pen.​

Answer 1

$2

Explanation:

Let the cost of a pen and a pencil be $x and $y respectively.

5x +3y= 13 -----(1)

5y + 3x= 11

3x +5y= 11 -----(2)

(1) ×5:

25x +15y= 65-----(3)

(2) ×3:

9x +15y= 33 -----(4)

(3) -(4):

25x +15y -(9x +15y)= 65 -33

Expand:

25x +15y -9x -15y= 32

Simplify:

16x= 32

Divide both sides by 16:

x= 32 ÷16

x= 2

Thus, a pen costs $2.