Question

difference between two numbers is 30twice the greater number is less then 7times the smaller number by 5 find the numbers​

Answer 1

$\bf{\huge{\underline{\boxed{\tt\red{Answer:}}}}}$

Given :-

• Difference between two numbers is 30
• Twice the greater number is less then 7 times the smaller number by 5

To find :-

• The greater and the smaller number

Solution :-

Let the greater number be x

Let the smaller number be y

As per the first condition,

• Difference between two numbers is 30

Representing it mathematically, we get our first equation,

x - y = 30 ----> 1

As per the second condition,

• Twice the greater number is less then 7 times the smaller number by 5,

Let's represent it mathematically to get our second equation,

2x = 7y + 5

2x - 7y = 5 ---->2

Now, we will use elimination method to solve equations 1 and 2, simultaneously. But before that let's equate one of the terms of both the equations.

Multiply equation 1 by 2,

x - y = 30

2 × x - 2 × y = 2 × 30

2x - 2y = 60 ---->3

Solve equations 2 and 3 simultaneously by subtracting equation 3 from 2,

...2x - 2y = 60 -----> 3

- (2x - 7y = 5)-------> 2

--------------------------

5y = 55

y = $\bf\large\frac{55}{5}$

y = 11

•°• Smaller number, y = 11

Substitute y = 11 in equation 1,

x - y = 30

x - 11 = 30

x = 30 + 11

x = 41

•°• Greater number, x = 41

•°• The numbers are : 41 and 11

$\bf{\huge{\underline{\boxed{\rm{\blue{Verification:}}}}}}$

For first case :-

• Difference between two numbers is 30

Numbers = 41 & 11

Difference = 30

Let's see if the condition is satisfied,

41 - 11 = 30

30 = 30

LHS = RHS

For second case :-

• Twice the greater number is less then 7 times the smaller number by 5

Greater number = 41

Twice the greater number = 2 (41) = 82

Smaller number = 11

Seven times the smaller number = 7 (11) = 77

Let's check whether the condition is satisfied,

82 = 77 + 5

82 - 77 = 5

5 = 5

LHS = RHS

Hence our answer is right.