1. Price of a pen and a notebook together is 25 rupees.
Price of 4 pens and a notebook is 40 rupees.
a. What is the price of 3 pens?
b. What is the price of a notebook?

2. Look at the equations given below:
x + 2y = 27
2x + y = 24
a. What is the value of 3x + 3y?
b. What is the value of x + y?

3. One side of a rectangle is 5 cm more than the other side.
Perimeter of the rectangle is 34 cm.
a. If the smaller side is x and the other is y, write the equations.
b. Find the lengths of the sides.

The price of 3 pens is 15 rupees and the price of a notebook is 20 rupees. For the second problem, the value of 3x + 3y is 51, and the value of x + y is 17. The sides of the rectangle are 6 cm and 11 cm.
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Answered by Anonymous | 2025-07-04

Question 1:
Let's solve the problem step-by-step:
Given:

Price of a pen and a notebook together is 25 rupees.
Price of 4 pens and a notebook is 40 rupees.

Let's denote the price of a pen by p and the price of a notebook by n .
Equations:

p + n = 25
4 p + n = 40

To find the price of 3 pens, we will first find p by solving the equations.
Subtract Equation 1 from Equation 2: ( 4 p + n ) − ( p + n ) = 40 − 25 3 p = 15 p = 5
Now that we have p , the price of a single pen is 5 rupees.
a. What is the price of 3 pens?
3 p = 3 × 5 = 15 rupees.
b. What is the price of a notebook?
Substitute p = 5 back into Equation 1: 5 + n = 25 n = 20
So, the price of a notebook is 20 rupees.
Question 2:
Given equations:

x + 2 y = 27
2 x + y = 24

These equations will help us find x and y .
Let's solve them step-by-step:
To eliminate y , let's multiply Equation 2 by 2: 2 ( 2 x + y ) = 2 × 24 4 x + 2 y = 48
Now, subtract Equation 1: ( 4 x + 2 y ) − ( x + 2 y ) = 48 − 27 3 x = 21 x = 7
Substitute x = 7 back into Equation 2: 2 × 7 + y = 24 14 + y = 24 y = 10
a. What is the value of 3x + 3y?
3 x + 3 y = 3 × 7 + 3 × 10 = 21 + 30 = 51
b. What is the value of x + y?
x + y = 7 + 10 = 17
Question 3:
Given:

One side of a rectangle is 5 cm more than the other side.
Perimeter of the rectangle is 34 cm.

Let's denote the smaller side as x and the other side as y .
a. Write the equations:

y = x + 5
2 x + 2 y = 34

Substitute Equation 1 into Equation 2: 2 x + 2 ( x + 5 ) = 34 2 x + 2 x + 10 = 34 4 x + 10 = 34 4 x = 24 x = 6
Now, substitute x = 6 back into Equation 1: y = 6 + 5 = 11
b. Find the lengths of the sides: The smaller side x is 6 cm, and the other side y is 11 cm.

Answered by SophiaElizab | 2025-07-07