Question

Two number differ by 3.the sum of twice the smaller number and twice The greater number is 19.find the number​

Answer 1

Answer:

Greater Number = 6.25

Smaller Number = 3.25

Given:

Difference of two numbers = 3.

Sum of twice the smaller and twice the greater number = 19

To Find:

The value of two numbers

Explanation:

Let the greater number be x and smaller number be y respectively.

ATQ,

x - y = 3 ......(1)

2x + 2y = 19 .....(2)

Multiplying equation (1) by 2 , we get:

2x - 2y = 6 .....(3)

Adding equation (2) and (3) , we get:

2x + 2y + 2x - 2y = 19 + 6

4x = 25

x = $\dfrac{25}{4}$

x = 6.25

Substituting the value of x in equation (1) , we get:

6.25 - y = 3

-y = -3.25

y = 3.25

Proof:

Equation 1:

x - y = 3

6.25 - 3.25 = 3

3 .= 3

LHS = RHS

Hence Proved

Equation 2:

2x + 2y = 19

2*6.25 + 2*3.25 = 19

12.5 + 6.5 = 19

19 = 19

LHS = RHS

Hence Proved