The sum of two numbers is 80. The larger number exceeds four times the smaller one by 5. Find the numbers.

Let the larger number be x and the smaller number be y. 

Then as per the question 

x + y = 80 …….(i) 

x = 4y + 5 

x – 4y = 5 …….(ii) 

Subtracting (ii) from (i), we get 

5y = 75 

⇒ y = 15 

Now, putting y = 15 in (i), we have 

x + 15 = 80 

⇒ x = 65 

Hence, the numbers are 65 and 15.

Let x be the first number and y be the second number.

As per statement,

x + y = 80 and

x – 4y = 5

on subtracting both the equations, we get

y = 15

From (1): x + 15 = 80

x = 80 – 15 = 65

Answer:

Required numbers are 15 and 65.

Let the smaller number is x and larger number is y. 

Given that sum of both numbers is 80. 

∴ x + y = 80. ... (1) 

Given that the larger number exceeds four times the smaller one by 5. 

∴ y = 4x +5. ... (2) 

By putting y = 4x + 5 in equation (1), we get x + (4x +5) = 80. 

⇒ 5x = 80 – 5 = 75 

⇒ x = \(\frac{75}{5}\) = 15. 

Now, putting x = 15, in equation (2), we get 

y = 4 × 15 + 5 = 60 + 5 = 65. 

Hence, the numbers are 15 and 65.

Let the larger number be x and the smaller number be y. 

Then as per the question 

x + y = 80 …….(i) 

x = 4y + 5 

x – 4y = 5 …….(ii) 

Subtracting (ii) from (i), we get 

5y = 75 ⇒ y = 15 

Now, putting y = 15 in (i), we have 

x + 15 = 80 ⇒ x = 65 

Hence, the numbers are 65 and 15.