Question

The sum of two numbers is 145 and their difference is 33. Find the numbers?

Answer 1

Aɴsᴡᴇʀ

given :-

• sum of two numbers = 145
• difference of two numbers = 33

to find :-

• find the numbers ?

solution :-

• let the numbers be x and y

according to the question;

• sum of numbers = 145

➪ x + y = 145 ......(i)

and

• difference of numbers = 33

➪ x - y = 33 ......(ii)

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now we have two equations:

• x + y = 145 .........(i)
• x - y = 33 ...........(ii)

now solve these equations by elimination method;

adding (i) and (ii)

➪ x + y + (x - y) = 145 + 33

➪ x + y + x - y = 178

➪ x + x = 178

➪ 2x = 178

➪ x = 178/2

➪ x = 89

now, substitute the value of x in (i)

x + y = 145

➪ 89 + y = 145

➪ y = 145 - 89

➪ y = 56

therefore, numbers are 89 and 56

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verification :-

x + y = 145

→ 89 + 56 = 145

→ 145 = 145

and

x - y = 33

→ 89 - 56 = 33

→ 33 = 33

hence, verified!