1.

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

Answer»

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.



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