Question

Practice EXERCISE 2.2
1. The sum of two numbers is 45 and their ratio is 7: 8. Find the numbers.
The sum of two​

Answer 1

Answer:

21 and 24

Explanation

Given

Sum of two numbers = 45

ratio of the numbers = 7:8

To find

The two numbers

Solution

Let,

The two numbers are 7x and 8x

Acc to the question

$\mathsf{7x + 8x = 45}$

$\mathsf{15x = 45}$

$\mathsf{x = \dfrac{45}{15}}$

$\mathsf{x = 3}$

The First number = 7x

$\mathsf{\implies 7(3)}$

$\mathsf{\implies 21}$

The second number = 8x

$\mathsf{\implies 8(3)}$

$\mathsf{\implies 24}$

____________________

$\mathbf{Verification:-}$

Add the two numbers.. If you get the sum as 45. Then, the answer is correct

let us add

$\mathsf{\implies 21 + 24}$

$\mathsf{\implies 45}$

Hence, the two numbers are 21 and 24 respectively

Answer 2

Que. The sum of two numbers is 45 and their ratio is 7: 8. Find the numbers.The sum of two.

$\boxed{\boxed{\huge{\bf{Answer}}}}$

let the first number be x

and the second number be y

Now , as per the information given in the question

the sum of two numbers is 45 so,

x + y = 45

Let it be the equation (1)

Also the ratio of two numbers is 7:8 So,

$\bf{\frac{x}{y}}$ = $\bf{\frac{7}{8}}$

by cross multiplication

8x = 7y

Let this equation be equation (2)

Now, we will multiply equation (1) by 8

8(x + y = 45)

8x + 8y = 360

Now , From equation 1 we will put the value of 8x = 7y

7y + 8y = 360

15y = 360

$\boxed{\bf{ y = 24}}$

Now in equation 1 we will put the value of y = 24

x + y = 45

x + 24 = 45

x = 45 - 24

$\boxed{\bf{ x = 21}}$

And the sum of these two numbers is already given

$\boxed{\bf{21 + 24 = 45}}$