Mathematics solution NCERT
Class 9 - Chapter 2: Introduction to Linear Polynomials
Q1: Find the value of the linear polynomial 5x − 3 if:
(ii) x = -1
(iii) x = 2
Ans (i) Here we have, 5x − 3, now we will substitute x = 0:
5(0) − 3 = −3
Answer: −3
Ans (ii) Here we have, 5x − 3, now we will substitute x = −1:
5(−1) − 3 = −5 − 3 = −8
Answer: −8
Ans (iii) Here we have, 5x − 3, now we will substitute x = 2:
5(2) − 3 = 10 − 3 = 7
Answer: 7
Q2: Find the value of the quadratic polynomial 7s² − 4s + 6 if:
(ii) s = −3
(iii) s = 4
Ans (i) Here we have, 7s² − 4s + 6, now we will substitute s = 0:
7(0)² − 4(0) + 6 = 6
Answer: 6
Ans (ii) Here we have, 7s² − 4s + 6, now we will substitute s = −3:
7(−3)² − 4(−3) + 6
= 7(9) + 12 + 6
= 63 + 12 + 6
= 81
Answer: 81
Ans (iii) Here we have, 7s² − 4s + 6, now we will substitute s = 4:
7(4)² − 4(4) + 6
= 7(16) − 16 + 6
= 112 − 16 + 6
= 102
Answer: 102
Q3: The present age of Salil's mother is three times Salil's present age. After 5 years, their ages will add up to 70 years. Find their present ages.
Solution:
Let Salil's present age be x years.
Then Mother's present age = 3x years.
After 5 years:
Salil's age = x + 5
Mother's age = 3x + 5
According to the question:
(x + 5) + (3x + 5) = 70
4x + 10 = 70
4x = 60
x = 15
Mother's age = 3 × 15 = 45
Answer: Salil = 15 years, Mother = 45 years.
Q4: The difference between two positive integers is 63. The ratio of the two integers is 2 : 5. Find the two integers.
Solution:
Let the integers be 2x and 5x.
Difference = 63
5x − 2x = 63
3x = 63
x = 21
First integer = 2 × 21 = 42
Second integer = 5 × 21 = 105
Answer: 42 and 105
Q5: Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total ₹88, how many coins does she have of each type?
Solution:
Let the number of five-rupee coins be x.
Number of two-rupee coins = 3x
Total value:
5x + 2(3x) = 88
5x + 6x = 88
11x = 88
x = 8
Five-rupee coins = 8
Two-rupee coins = 24
Answer: 8 five-rupee coins and 24 two-rupee coins.
Q6: A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?
Solution:
Let the shorter piece be x feet.
Longer piece = 4x feet.
Total length = 300 feet
x + 4x = 300
5x = 300
x = 60
Longer piece = 4 × 60 = 240
Answer: Shorter piece = 60 feet, Longer piece = 240 feet.
Q7: If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?
Solution:
Let the width be x cm.
Length = 2x + 3 cm.
Perimeter = 24 cm
2(Length + Width) = 24
Length + Width = 12
(2x + 3) + x = 12
3x + 3 = 12
3x = 9
x = 3
Length = 2(3) + 3 = 9
Answer: Width = 3 cm, Length = 9 cm.