How do you solve this problem?

The avera&e (aritmeticmean)of x and y is 5 and the avera&e of x, y, and z is 8. What is the value of z?

(a)19
(b)14
(c)13
(d)11
(e)3 I solved it by addin 8+5=13
So I chose (c)13. But it's wron& and the answer is (b)14. How did they arrive at that answer?????

You should solve it by two fives + z=24

why do i have to solve it this way?

5+5+z=24
10+z=24
-10 -10
z=14

You need to solve it this way because the average of x, y, and z is 8. This means that if you add up the values of x, y, and z and divide by 3, the result should be 8.

Let's break down the problem step by step:

1. The average of x and y is 5. This means that (x + y) / 2 = 5. Multiplying both sides by 2 gives you x + y = 10.

2. The average of x, y, and z is 8. This means that (x + y + z) / 3 = 8. Multiplying both sides by 3 gives you x + y + z = 24.

3. Now you can solve for z by subtracting the equation from step 1 from the equation from step 2.

(x + y + z) - (x + y) = 24 - 10
z = 14

Therefore, the value of z is 14, which corresponds to option (b).