Mathematics
The sum of two positive numbers x and y (x > y) is 50 and the difference of their squares is 720. Find the numbers.
Linear Equations
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Answer
Given,
Sum of numbers = 50
∴ x + y = 50
⇒ x = 50 - y ………(1)
Difference of squares = 720
∴ x2 - y2 = 720
⇒ (50 - y)2 - y2 = 720
⇒ 502 + y2 - 2 × 50 × y - y2 = 720
⇒ 2500 - 100y = 720
⇒ 100y = 2500 - 720
⇒ 100y = 1780
⇒ y = = 17.80
Substituting value of y in equation (1), we get :
⇒ x = 50 - y = 50 - 17.80 = 32.20
Hence, numbers are 32.20 and 17.80
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