Mathematics Solutions Solutions for Class 6 Math Chapter 10 - Equations

Answer:

16 ÷ 2 = 8

5 × 2 = 10

9 + 4 = 13

72 ÷ 3 = 24

4 + 5 = 9

8 × 3 = 24

19 − 10 = 9

10 − 2 = 8

37 − 27 = 10

6 + 7 = 13

So,

16 ÷ 2 = 10 − 2

5 × 2 = 37 − 27

9 + 4 = 6 + 7

72 ÷ 3 = 8 × 3

4 + 5 = 19 − 10

Answer:

(1)
Let the certain number be x.

∴ Sum of a certain number and 3 = x + 3

(2)
Let another number be x.

∴ Difference obtained by subtracting 11 from another number = x − 11

(3) 
Let another number be x.

∴ Product of 15 and another number = 15 × x = 15x

(4)
Let the number be x.

Four time a number = 24

∴ 4 × x = 24

⇒ 4x = 24

Answer:

(1) Subtract 9 from both sides

x + 9 = 11         

⇒ x + 9 − 9 = 11 − 9               (Subtract 9 from both sides)

⇒ x + 0 = 2

⇒ x = 2

(2) Add 4 to both sides

x − 4 = 9 

⇒ x − 4 + 4 = 9 + 4         (Add 4 to both sides)

⇒ x + 0 = 13

⇒ x = 13

(3) Divide both sides by 8

8x = 24

⇒ $\frac{8x}{8}=\frac{24}{8}$          (Divide both sides by 8)

⇒ x = 3

(4) Multiply both sides by 6

$\frac{x}{6}= 3$

⇒ $\frac{x}{6}\times 6= 3\times 6$             (Multiply both sides by 6)

⇒ x = 18

Answer:

Answer:

(1) 
y − 5 = 1

⇒ y − 5 + 5 = 1 + 5         (Add 5 to both sides)

⇒ y + 0 = 6

⇒ y = 6

Thus, the solution of the given equation is y = 6.

(2)
8 = t + 5

⇒ 8 − 5 = t + 5 − 5         (Subtract 5 from both sides)

⇒ 3 = t + 0

⇒ 3 = t

Thus, the solution of the given equation is t = 3.

(3)
4x = 52

⇒ $\frac{4x}{4}=\frac{52}{4}$            (Divide both sides by 4)

⇒ x = 13

Thus, the solution of the given equation is x = 13.

(4)
19 = m − 4

⇒ 19 + 4 = m − 4 + 4         (Add 4 to both sides)

⇒ 23 = m + 0

⇒ 23 = m

Thus, the solution of the given equation is m = 23.

(5)
$\frac{p}{4}=9$

⇒ $\frac{p}{4}\times 4=9\times 4$        (Multiply both sides by 4)

⇒ p = 36

Thus, the solution of the given equation is p = 36.

(6)
x + 10 = 5

⇒ x + 10 − 10 = 5 − 10            (Subtract 10 from both sides)

⇒ x + 0 = −5

⇒ x = −5

Thus, the solution of the given equation is x = −5.

(7)
m − 5 = −12

⇒ m − 5 + 5 = −12 + 5           (Add 5 to both sides)

⇒ m + 0 = −7

⇒ m = −7

Thus, the solution of the given equation is m = −7.

(8)
p + 4 = −1

⇒ p + 4 − 4 = −1 − 4           (Subtract 4 from both sides)

⇒ p + 0 = −5

⇒ p = −5

Thus, the solution of the given equation is p = −5.

Answer:

(1)
Let the number of sheeps with Haraba at first be x.

According to the given condition, 

Number of sheeps with Haraba at first − Number of sheeps sold in the market = Number of sheeps left with Haraba

∴ x − 34 = 176

⇒ x − 34 + 34 = 176 + 34          (Add 34 to both sides)

⇒ x + 0 = 210

⇒ x = 210

Thus, there were 210 sheeps with Haraba at first.

(2)
Let the total number of jam bottles made by Sakshi be x.

According to the given condition, 

Total number of jam bottles made by Sakshi − Number of jam bottles given to her friends = Number of jam bottles left with Sakshi

∴ x − 7 = 12

⇒ x − 7 + 7 = 12 + 7          (Add 7 to both sides)

⇒ x + 0 = 19

⇒ x = 19

So, the total number of jam bottles made by Sakshi are 19.

Weight of jam in each bottle = 250 g

∴ Total weight of the jam

= Weight of jam in each bottle × Number of bottles

= 250 g × 19

= 4750 g

= 4.75 kg            (1 kg = 1000 g)

Thus, the total weight of the jam made by Sakshi is 4750 g or 4.75 kg.

(3) 
Let the weight of wheat bought by Archana altogether be x kg.

According to the given condition, 

Weight of wheat bought by Archana altogether − Weight of the wheat used in 3 months = Amount of wheat left with Archana

∴ x kg − 12 kg/month × 3 months = 14 kg

⇒ x − 36 = 14

⇒ x − 36 + 36 = 14 + 36          (Add 36 to both sides)

⇒ x + 0 = 50

⇒ x = 50

Thus, the weight of wheat bought by Archana altogether is 50 kg.