Question

5. Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
6. Three consecutive integers add up to 51. What are these integers?​

Answer 1

Answer

5. The numbers are 27 and 45

6. The required integers are 16 , 17 and 18

$\bf \large \underline{Solution : }$

Answer to Question 5

Let the numbers be x and y respectively

Given , the numbers differs by 18 :

$\sf \implies x - y = 18 \\ \\ \implies \sf x = 18 + y$

Again , the ratio of the numbers is 5:3

$\implies \sf (y + 18):y = 5 : 3 \\ \\ \sf \implies \dfrac{y + 18}{y } = \dfrac{5}{3} \\ \\ \sf\implies 3y + 54 = 5y \\ \\ \sf \implies 5y - 3y = 54 \\ \\ \sf \implies 2y = 54 \\ \\ \sf \implies y = 27$

And the other number is :

$\sf\implies x =18 + 27 \\\\ \sf\implies x = 45$

Therefore , the required numbers are 27 and 45

______________________

Answer to question 6

Let the consecutive integers be x - 1 x and x+1 respectively.

According to question

$\sf\implies x-1 + x + x+1 = 51 \\\\ \sf\implies 3x = 51 \\\\ \sf\implies x = 17$

Therefore , required integers are 17-1 , 17 and 17+1 i.e. 16 , 17 , 18

Answer 2

$\bf \huge{ \underline{ \underline{ \purple{answer}}}}$

5)Given:-

★Two numbers ratio is 5:3

★Two number difference is 18.

Solution:-

$\bf \: according \: to \: the \: question$

$\bf \implies \blue{ 5x - 3x = 18}$

$\bf \implies \blue{2x = 18}$

$\bf \implies \blue{x = \frac{18}{2} }$

$\bf \implies \blue{x = 9}$

therefore, the two numbers are,

$\bf \red{5x = 5 \times 9 = 45}$

$\bf \red{3x = 3 \times 9 = 27}$

$\bf \huge \fbox \green{ \: \: \: two \: numbers \: are \: 45 \: and \: 27 \: \: \: }$

6)Given:-

★sum of numbers is 51.

Solution:-

$\bf \: let \: the \: three \: consecutive \: number \: is \: x \: ,x + 1 \: and \: x + 2$

sum of numbers is 51

$\bf \blue{ \therefore \: x + x + 1 + x + 2 = 51}$

$\bf \blue{3x + 3 = 51}$

$\bf \blue{3x = 48}$

$\bf \blue{x = 16}$

The numbers are x=16

x+1=16+1=17

x+2=16+2=18.

$\bf \huge \fbox \green{ \: \: \: consecutive \: integers \: are \: 16 ,\: 17 \: and \: 18 \: \: \: }$