Question

There are two numbers such that the sum of the numbers is 48 and their difference is 8. Find the difference of their squares​

Answer 1

Answer:

384

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Answer 2

Answer:

Difference of the squares of the two numbers is 384.

Step-by-step explanation:

Given :-

• There are two numbers.
• The sum of the numbers is 48.
• Difference of the numbers is 8.

To find :-

Difference of their squares.

Solution :-

⇒ Let the two numbers be x and y.

ATP :

• x + y = 48 - i)
• x - y = 8 - ii)

Using substitution method :

• x + y = 48
• x = 48 - y

Place the value of x in ii) :

⇒ (48 - y) - y = 8

⇒ 48 - y - y = 8

⇒ 48 - 2y = 8

⇒ 48 - 8 = 2y

⇒ 40 = 2y

⇒ y = 20

Place the value of y in i) :

⇒ x + y = 48

⇒ x + 20 = 48

⇒ x = 28

Difference of their squares :

⇒ (28)² - (20)²

⇒ 784 - 400

⇒ 384

∴ Difference of the squares of the two numbers is 384.