Question

The average of five numbers is 10.2. the average of first two numbers is half of third number and the average of third and fourth number is 12.5. if the fourth number is 13. find the fifth number.

Answer 1

please mark it as a brainliest answer

Answer 2

Answer: The fifth number is 14.

Step-by-step explanation:

Let the given five numbers are,

a, b, c, d, e

According to the question,

The average of five number = 10.2

$\implies \frac{a+b+c+d+e}{5}=10.2$

$\implies a+b+c+d+e=51$ ----- (1)

Also,

The average of first two numbers is half of third number,

$\implies \frac{a+b}{2}=\frac{c}{2}\implies a+b=c$ -----(2)

Now, the average of third and fourth number is 12.5.

$\implies \frac{c+d}{2}=12.5$

$\implies c+d=25$ -----(3)

Since, the fourth number is 13 ⇒ d = 13,

By equation (3),

c = 25 - 13 = 12,

By equation (2),

a+b = 12,

By substituting all values in equation (1),

12 + 12 + 13 + e = 51,

⇒ 37 + e = 51,

⇒ e = 14

Thus, the fifth number is 14.