myhelper: Linear Equation with one Variable

Exercise 7 B

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Question 1

The sum of Ritu age and Ashu age is 25. Ritu is 12 years old . Write an equation to find ashu age ?

Sol: Let Ritu age =x ; Ashu age = y

Acc. to question = x+y=25

= $12+y=25 \Rightarrow y=25-12=13$

Ashu age = 13 year

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Question 2

A number decreased by 4 is equal to -6 . find the number

Sol: Let the number =x

Acc. to question x-4=-6

$ \Rightarrow x=-6+4 \Rightarrow x=-2$

The number =- 2 Ans

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Question 3

7 times a number decreased by 3 equal to 18. find the number

Sol :

Let the number= x

$\Rightarrow 7 \times x-3=18 $

$\Rightarrow 7 x=18+3$

$\Rightarrow 7 \times x=21 $

$\Rightarrow x=\frac{21}{7} \Rightarrow x=3$

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Question 4

One- fifth of a number is 9. find the number

Sol :

Let the number =x

Acc. to question = $\frac{1}{5} \times x=9$

$x=9 \times 5 \quad \Rightarrow x=45$

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Question 5

How old is ramesh if 10 year ago he was 25 year old ?

Sol :

Age of ramesh 10 year ago = 25 year

∵ Age of ramesh , after 10 year = 25 + 10 = 35 year

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Question 6

Apporv received three-fourths of all votes cast in the election far school president. If he received 876 votes, how many student voted ?

Sol :

Apoorv received votes = 876

Let total number of votes = x

Acc. to question = $\frac{3}{4} \times x=876$

x= $876 \times \frac{4}{3}=1168$

Total No, of votes = 1168 votes of students

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Question 7

After gaining 15 kg , Nisha weight 60 kg . What was her previous weight ?

Sol: Let the previous weight of Nisha = x

Weight gained = 15kg

x+ 15 =60 = x= 60 -15 =45kg

Previous weight = 45kg answer

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Question 8

A pole x meters long is broken into two parts, One part is 5 meters long.

(i) What is the length of the other parts?

(ii) If the other part is 6 meters long. write an equation and use it to find the value of x

Sol: (i) Length of pole = x m

other part = (x-5) m answer

(ii) If the other part = x-5

Acc , to Question = x -5 = 6

=x=6+5 = 11m

Length of pole = 11m answer

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Question 9

The teacher tells the class that the highest marks obtained by a student in her class in three times the lowest marks minus seven . If the highest marks are 86 , find the lowest marks.

Sol: Let the lowest marks = x

Acc. to question= $3 x-7=86 \Rightarrow 3 x=86+7 .$

$3 x=93 \Rightarrow x=\frac{93}{3}=31$

∵ Lowest marks = 31

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Question 10

Benny thinks of a number subtracts 18 from it and divides the difference by 3. The result is -4 . what is the number ?

Sol: Let the number =x

$\frac{x-18}{3}=-4 \Rightarrow x-18=-4 \times 3$

$\Rightarrow \quad x-18=-12 \quad x=-12+18$

$\Rightarrow \quad x=6 \quad$ Numbcr $=6$ answer

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Question 11

Mr. Grover is three times as old as his son and the sum of their age is 48 . How old is each ?

Sol: Let the age of son = x

Age of Mr. Grover= 3x

$\Rightarrow \quad 3 x+x=48 \Rightarrow 4 x=48 .$

$\Rightarrow \quad x=\frac{48}{4}=12$ years $\therefore$ Son age = 12 years answer

= Mr. Grover age $=3 \times 12=36$ years

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Question 12

Sunil is 48 years old . He is 7 years less than 5 times his daughter's age . What is his daughter's age ?

Sol: Let daughter age =x

$\Rightarrow 5 x-7=48 \Rightarrow 5 x=48+7 \Rightarrow 5 x=55$

$\Rightarrow x=\frac{55}{5} \Rightarrow x=11$ years

daughter's age = 11 y answer

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Question 13

A number is 6 more than two times another number. The sum of tthe two number is 24. Find the number

Sol: Let one number =x ; Other = y = 2x +6

$x+y=24 \Rightarrow x+2 x+6=24$

$3 x=24-6 \quad \Rightarrow \quad 3 x=18 \quad \Rightarrow x=\frac{18}{3}=6$

x =6 ; y = 2x +6 = $2 \times 6+6=12+6=18$

y = 18 answer

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Question 14

Four times Sonu age decrease by 3 is equal to 3 times his age increased by 7. How old is sonu?

Sol :

Sonu age =x

$\Rightarrow 4 x-3=3 x+7$

$\Rightarrow 4 x-3 x=7+3$

$\Rightarrow x=10$ years

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Question 15

Find the 3 Consecutive number whose sum is 81

Sol :

Number are x, x+1 , x+2

$x+x+1+x+2=81$

3x+3=81

$3 x=81-3$

$3 x=78 \Rightarrow x=\frac{78}{3}$

x=26

x +1 = 26+ 1 = 27

x+2 =26+ 2 = 28 answer

Exercise 7A

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Question 1

Solve the following equations by transposition :

(i) x+5=9

Sol: x=9-5=4

(ii) a+10=12

Sol: a= 12 -10=2

(iii) $x+\frac{3}{5}=\frac{4}{5}$

Sol: $\Rightarrow x=\frac{4}{5}-\frac{3}{5}$

$\Rightarrow x=\frac{4-3}{5}=\frac{1}{5}$

(iv) n+1.8=3

Sol: $n=3-1.8$

n=1.2

(v) x-7=4

Sol: $\Rightarrow 2=4+7=11$

(vi) $x-4.2=11.4$

Sol: $x=11.4+4.2$

$x=15.6$

(vii) $-12+a=23$

Sol: $a=23+12=35$

(viii) $P-\frac{2}{7}=\frac{4}{7}$

Sol: $P=\frac{4}{7}+\frac{2}{7}$

$P=\frac{6}{7}$

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Question 2

Solve each equation:

(i) 3y=9

Sol: $y=\frac{9}{3}=3$

(ii) 7y=75

Sol: $y=\frac{75}{5}=15$

(iii) -7a =84

Sol: $a=\frac{84}{-7}=-12$

(iv) $-8 m=-24$

Sol: $m=\frac{-24}{-8}=3$

(v) $\frac{j}{7}=5$

Sol: $j=7 \times 5=35$

(vi) $\frac{x}{2}=-10$

Sol: $x=-10 \times 2=-20$

(vii) $\frac{w}{-8}=-4$

Sol: w=$-4\times -8$

w=32

(viii) $\frac{g}{2.9}=10$

Sol: $g=10 \times 2.9$

$g=29 Ans$

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Question 3

Write the following statements in equation form. Find numerals to make true statements.

(i) The sum of 5 and x is 12

Ans: equation form = 5 +x =12

Sol: 7

(ii) x decreased by 7 is 13

Ans: equation form= x-7=13

Sol: 20

(iii) Six less than two times $y$ is 32

Ans: equation form= $2 y-6=32$

Sol: $2 y=38 ; y=19$

(iv) If 8 is taken away from the number $n$, the result is $-4$

Ans: equation form= $n-8=-4$

Sol: n=4

(v) 9 multiplied by r is 36

Ans: equation form =$9 \times r=36$

Sol: r=4

(vi) q multiplied by 7 gives-35

Ans: $9 \times 7=-35$

Sol: q=-35

(vii) If d is divided by -4 the result is 3

Ans: $d \div-4=3$

Sol: $d=-4 \times 3=-12$

(viii) Eight decreased by 3 times a number equals 2.

Sol :

Equation : 8-3x=2

-3x=2-8

-3x=-6

$x=\frac{-6}{-3}=2$

x=2

(ix) The product of 7 and the number x is 42

Ans: $7 \times x=42$

Sol: x=6

(x) Quotient of m divided by 5 is 6.

Ans: $\frac{m}{5}=6$

Sol: $m=5 \times 6=30$

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Question 4

Solve the following equation:

(i) $5 x+2=3 x+12$

Sol: $5 x-3 x=12-2$

= $2 x=10 \Rightarrow x=\frac{10}{2}=5$

(ii) $6 y-9=2 y+15$

Sol: $6 y-2 y=15+9$

=$4 y=24$

$y=\frac{24}{4} \quad \Rightarrow \quad y=6$

(iii) $2 x-3=9-x$

Sol: $\Rightarrow 2x+x=9+3$

$\Rightarrow \quad 3x=12$

$\Rightarrow \quad x=\frac{12}{3}$

$x=4$

(iv) $2 a-5=8 a+1$

Sol: $2 a-8 a=5+1$

$\begin{aligned}-6 a &=6 \\ a &=\frac{6}{-6} \\ a &=-1 \end{aligned}$

(v) b+3=33-b

Sol: $b+b=33-3$

$\begin{aligned} 2 b &=30 \\ b &=\frac{30}{2} \\ b &=15 \end{aligned}$

(vi) 1.9x+3.6 =2.5x+3

Sol: 1.9x-2.5x = 3-3.5

$\begin{aligned}-0.6 x &=-0.6 \\ x &=-\frac{0.6}{0.6} \end{aligned}$

x=1

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Question 5

Solve the following equations

(i) $6 x+14=16$

Sol: $\Rightarrow 6 x=16-14$

$\Rightarrow 6 x=2$

$\Rightarrow \quad x=\frac{2}{6}$

$\Rightarrow \quad x=\frac{1}{3}$

(ii) $7+5 x-3 x=21$

Sol: $2x=21-7$

$2x=14$

$x=\frac{14}{2}$

$x=7$

(iii) $1.2 x+4.8x=18$

Sol: $6 x=18$

$x=\frac{18}{6}=3$

(iv) $6(5 x-2)+12=30$

Sol: $30 x-12+12=30$

$30 x=30$

$x=\frac{30}{30}=1$

(v) $7(x-4)+13=6$

Sol: $\Rightarrow 7 x-28+13=6$

$\Rightarrow 7 x-15=6$

$\Rightarrow 7 x=6+15$

$\Rightarrow \quad x=\frac{21}{7}=3$

(vi) $5(6 x+1)=3(-8+x)+2$

Sol: $30 x+5=-24+3 x+2$

$\Rightarrow 30 x-3 x=-24+2-5$

$\Rightarrow 27 x=-27$

$\Rightarrow \quad x=\frac{-27}{27}=-1$

(vii) $4-4(x-5)=2(2-x)-6$

Sol: $\Rightarrow 4-4 x+20=4-2 x-6$

$\Rightarrow-4 x+2 x=4-6-4-20$

$\Rightarrow-2 x=-26$

$\Rightarrow-2 x=-26 \Rightarrow x=-\frac{26}{-2} \Rightarrow x=13$

(viii) $10 y-0.2(7-y)=19$

Sol:$\Rightarrow 10 y-1.4+0.2 y=19$

$\Rightarrow 10.2 y=19+1.4$

$\Rightarrow y=\frac{20.4}{10.2}$

$\Rightarrow y=2$

(ix) $\frac{12-x}{5}=x$

Sol: $\Rightarrow 12-x=5 x$

$\Rightarrow 12=54+x$

$\Rightarrow 12=64$

$\Rightarrow x=\frac{12}{6}$

SChand Composite Mathematics Class 7 Chapter 7 Linear Equation with one Variable Exercise 7B

Exercise 7 B

SChand Composite Mathematics Class 7 Chapter 7 Linear Equation with one Variable Exercise 7A

Exercise 7A

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