If the sum of its number is 80 rhen find their mean​

First number = 50, Second number = 30

Solution:

Assuming that the numbers are integers, let p denote the first number and q the second number.

Given, sum of the two numbers is 80.

∴ p+q = 80………………………………………………………………………………………………(1)

⇒ q = 80 - p ………………………………………………………….………………………………..(2)

Also given, 3 times the first number (p) is same as 5 times the second number (q).

∴ 3p = 5q ………………………………………………………………………………………………..(3)

Simultaneous solution of equations (1) and (3) in the two variables p and q will furnish the answer.

Method 1: Substitution Method

Substituting for q from (2) in (3),

3p = 5(80-p)

Or, 3p = 5x80 - 5p = 400 - 5p

Or, 8p = 400 (Transposing -5p from right to left and simplifying)

Or, 8p/8 = 400/8 (Dividing both sides by 8)

Or, 1.p = 50x8/8 (Factoring 400)

⇒ p = 50

Substituting for p = 50 in (2),

q = 80 - 50

⇒ q = 30

Method 2: Elimination Method

Rewriting, (2)→

3p - 5q = 0 ……………………………………………………………………………………………..…(4)

Now 3 x equation(1) - equation(4) →

3p + 3q -3p + 5q = 3x80 - 0

Or, 8q = 240

Dividing both sides by 8 and simplifying give

q = 30

Substituting for q=30 in (1),

p+30 = 80

Subtracting 30 from both sides,

p+30–30 = 80–30

Or, p+0 = 50

⇒p = 50

These values are in agreement with those obtained by method 1.

Hence, the first number = 50 and second number = 30 (Answer)

Result Verification:

p = 50, q= 30

∴ p+q = 50+30 = 80 in agreement with equation (1)

3p = 3x50 = 150

5q = 5x30 = 150

Step-by-step explanation: