Question

Difference between two numbers is 30. Twice the greater number is less than 7 times the smaller number by 5. Find the numbers.
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Answer 1

Step-by-step explanation:

Given :-

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

To find :-

Find the numbers?

Solution :-

Let the two numbers be X and Y

Let X > Y

The greater number = X

The smaller number = Y

Given that

Difference between two numbers is 30.

=> X-Y = 30 --------(1)

=> X = 30+Y -------(2)

And

Twice the greater number is less than 7 times the smaller number by 5.

=> 2X - 7 Y = 5 ------(3)

From (2)

=> 2(30+Y) -7Y = 5

=> 60+2Y-7Y = 5

=> 60-5Y = 5

=>-5Y = 5-60

=> -5Y = -55

=> 5Y = 55

=> Y = 55/5

=> Y = 11

On Substituting the value of Y in (2)

=> X = 30+11

=> X = 41

Therefore, X = 41 and Y = 11

Answer:-

The required two numbers for the given problem is 41 and 11 respectively.

Check:-

The two numbers = 41 and 11

The difference between two numbers

=> 41-11

=> 30

Difference between two numbers is 30.

and

Twice the greater number = 2×41 = 82

7 times the smaller number = 7×11 = 77

Their difference = 82-77 = 5

Twice the greater number is less than 7 times the smaller number by 5.

Verified the given relations in the given problem.