Question

The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil boxNCERT Class XMathematics - Exemplar ProblemsChapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Answer 1

Let the cost of pens be x, and the cost of pencil boxes be y respectively.
So, 4x+4y=100
Dividing throughout by 4
x+y=25 —(equation 1)
Now, 3x=15+y
.: 3x-y=15—(equation 2)
Now,multiply equation 1 by 3,we get
3x+3y=75—(equation 3)
Now Subtracting equation 2 from equation 3;
0x+4y=60
.: y=60/4
.:y=15
Substitute y in equation 1
x+15=25
.:x=25-15
.:x=10
.: The cost of pen is 10 and cost of pencil box is 15

Answer 2

Hey there !!

Cost of  1 pen = x
Cost of 1 pencil box = y

Given :-
4x + 4y = 100   
4 [ x + y ] = 100
x + y = 100 / 4
x + y = 25   -----> [ 1 ]

also ,
x = y +15        
x - y = 15         -----> [2]

we can solve this by any method :-
1) graphical method
2) substitution method
etc ...

lets use substitution method :-
  


x + y = 25
x = 25 - y

put this value in the equation below :-

 x - y = 15

25 - y - y = 15
25 - 2y = 15
25 - 15 = 2y
10 = 2y
y = 5

x + y = 25
x + 5 = 25
x = 25 - 5
x = 20

hence ,

x = 20
y = 5