Question

find two numbers whose sum is 30 and difference is 4
​

Answer 1

Answer :-

17 and 13.

Explanation :-

Given :

• Sum of two numbers = 30.
• Difference of two numbers = 4.

To Find :

• The Numbers.

Solution :

Let the two numbers be x and y.

According to the Question,

x + y = 30. — (i)

And,

x - y = 4. — (ii)

We can say that,

x = 30 ‐ y.

Substitute this value in equation (i).

➛ (30 - y) - y = 4.

➛ 30 - y - y = 4.

➛ 30 - 2y = 4.

➛ -2y = 4 - 30.

➛ -2y = -26.

➛ 2y = 26.

➛ y = 13.

Now, Calculating the value of x,

➛ x = 30 - y.

➛ x = 30 - 13.

➛ x = 17.

Therefore, The Numbers are 17 and 13.

Verification :

➛ x + y = 30.

➛ 17 + 13 = 30.

➛ 30 = 30.

And,

➛ x - y = 4.

➛ 17 - 13 = 4.

➛ 4 = 4.

LHS = RHS.

Hence, Verified.

Answer 2

Question:-

➡ Find two numbers whose sum is 30 and difference is 4.

Answer:-

➡ The numbers are 17 and 13.

Solution:-

This can be solved easily by substitution or elimination method.

Using substitution,

Let the numbers be x and y

So, as per the question,

x + y = 30 — (i)

and,

x - y = 4 — (ii)

From (i),

x = 30 - y

Substituting x in equation (ii), we get,

➡ 30 - y - y = 4

➡ 30 - 4 = 2y

➡ 2y = 26

➡ y = 13

Now,

x = 30 - y

= 30 - 13

= 17

Hence,

x = 17

y + 13

Using Elimination,

Let the numbers be x and y.

So, according to the given conditions,

x + y = 30 — (i)

and,

x - y = 4 — (ii)

Adding equations (i) and (ii), we get,

➡ x + y + x - y = 30 + 4

➡ 2x = 34

➡ x = 17

From (i),

x + y = 30

➡ 17 + y = 30

➡ y = 30 - 17

➡ y = 13

Hence,

x = 17

y = 13

Verification:-

Let us verify our result.

x = 17 and y = 13

So,

x + y

= 17 + 13

= 30

Also,

x - y

= 17 - 13

= 4

Hence, the numbers are 17 and 13 (Verified)

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