Question

Q1. The sum of two consecutive even numbers is 38. Find the numbers.

Q2. The sum of three consecutive odd numbers is 51. Find the numbers.

Q3. In a class of 42 students, the number of boys is 2/5 of the girls. Find The number of boys and girls in the class.

Q4. What should be added to twice the number -7/3 to get 3/7

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Answer 1

Answer:

1. let one number is x and other x+2

x+x+2 = 38

2x = 36

x = 18

x+2=20

So, one number is 18 and other number is 20

2. let numbers are x-1, x+1, x+3

x-1 + x+1 + x+3 = 51

3x+3=51

3x = 48

x = 16

Numbers are 15 ,17 ,19

3. let number of girls is x and number of boys is 2/5 of x

2/5x + x =42

2x+5x/5 = 42

7x = 210

x = 30

2/5x=12

Number of girls is 30 and number of boys 12

Answer 2

$\Large\purple{\sf{\underline{Answer \: no. \: 1 :-}}}$

Let the first number be x.

Then, second number = x + 2.

ATQ,

$\dashrightarrow\sf x + x + 2 = 38$

$\dashrightarrow\sf 2x + 2 = 38$

$\dashrightarrow\sf 2x = 38 - 2$

$\dashrightarrow\sf x = \large\frac{36}{2}$

$\dashrightarrow\sf x = 18$

Hence, the first number is 18 and the second number is (18 + 2) = 20.

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$\Large\purple{\sf{\underline{Answer \: no. \: 2 :-}}}$

Let the first number be x.

Then, second number = x + 2 and third number = x + 4.

ATQ,

$\dashrightarrow\sf x + x + 2 + x + 4 = 51$

$\dashrightarrow\sf 3x + 6 = 51$

$\dashrightarrow\sf 3x = 51 - 6$

$\dashrightarrow\sf x = \large\frac{45}{3}$

$\dashrightarrow\sf x = 15$

Hence, the first number is 15, the second number is (15 + 2) = 17 and the third number is (15 + 4) = 19.

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$\Large\purple{\sf{\underline{Answer \: no. \: 3 :-}}}$

Let the number of girls be x.

Then, number of boys = $\large\sf{\frac{2}{5} × x \rightarrow \frac{2x}{5}}$

ATQ,

$\dashrightarrow\sf x + \frac{2x}{5} = 42$

$\dashrightarrow\sf \frac{5x + 2x}{5} = 42$

$\dashrightarrow\sf \frac{7x}{5} = 42$

$\dashrightarrow\sf 7x = 42 × 5$

$\dashrightarrow\sf x = \frac{42 × 5}{7}$

$\dashrightarrow\sf x = 30$

Hence, the number of girls is 30 and the number of boys is $\sf (30 × \frac{2}{5} )$ = 12.

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$\Large\purple{\sf{\underline{Answer \: no. \: 4 :-}}}$

Twice of -7/3 is (-7/3 × 2) = -14/3.

Now, let the required number be x.

ATQ,

$\dashrightarrow\sf \frac{-14}{3} + x = \frac{3}{7}$

$\dashrightarrow\sf x = \frac{3}{7} - \frac{14}{3}$

$\dashrightarrow\sf x = \frac{-89}{21}$

Hence, the required number is -89/21.