Mathematics

Grade10

Easy

Question

# The cost of 4 pens and 4 pencil boxes is $100. Three times the cost of a pen is $15 more than the cost of a pencil box. The cost of a pen and a pencil box respectively are

- $15 and $8
- $10 and $15
- $12 and $10
- $16 and $12

Hint:

### In this question, we have to find the cost of Pen and pencil. Here the cost of 4 pens and 4 pencil is $100 and also 3 times cost of pen is $15 more than cost of a pencil box . Consider both them as variable and make the equation for solution.

## The correct answer is: $10 and $15

### Here we have to find that the cost of Pen and pencil,

Firstly , it is given at the cost of 4 pens and 4 pencil is $100 .

Lets pen be x and pencil be y respectively,

So , 4x + 4y = 100

Dividing by 4 both sides,

x + y = 25 ----(1)

And also 3 times cost of pen is $15 more than cost of a pencil box, so we can write,

3x = 15 + y

3x – y = 15 ----(2)

Adding eq(1) and eq(2), we get…

x + y = 25

+ 3x – y =15

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

4x = 40

x = 10

substitute x = 10 in eq( 1)

10 + y = 25

y = 25 – 10

y = 15

Therefore , The cost of Pen and pencil $10 and $15.

Or simply,

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

4x+4y=100

x+y=25 ...(1)

3x=y+15

3x−y=15 ...(2)

Adding (1) and (2), we get

4x=40

x=10

Substitute x=10 in equation (1) to get y=15

In this question, we have to make equation on the given date about ages. For making equations , considers the variable of given data and make more than 1 equation to solve.