Let P = (x + y)k. If P = 10 and k = 3

lheiannie07 wrote:Let P = (x + y)k. If P = 10 and k = 3, what is the average of x and y?

(A) 0
(B) 1/2
(C) 5/3
(D) 10/3
(E) 7/2

Can some experts help me find the best solution in this problem?

OA C

Ultimately, we want to solve for the average of x and y, or (x + y)/2. Initially, we're given 10 = (x + y) * 3
10/3 = x + y
1/2 * (10/3) = (x + y)/2
5/3 = (x + y)/2

The answer is C

Let P = (x + y)k. If P = 10 and k = 3, what is the average of x and y?

(A) 0
(B) 1/2
(C) 5/3
(D) 10/3
(E) 7/2

Hi lheiannie07,
Let's take a look at your question.

$$P\ =\left(x+y\right)k$$
$$10\ =\left(x+y\right)3$$
$$x+y=\frac{10}{3} ... (i)$$

We know that average of x and y can be calculated as,
$$Average\ =\ \frac{x+y}{2}$$

Plugin the value of x+y from eq(i), we get:
$$Average\ =\ \frac{10}{3\times2}$$
$$Average\ =\ \frac{5}{3}$$

Therefore, option C is correct.

Hope it helps.
I am available if you'd like any follow up.