Question

Of three numbers, two are 1/2 and 1/3. What should the third number be so that the average of all is 1?

Answer 1

Step-by-step explanation:

There are three numbers namely x, y, and z.

y and z were given as 1/2 and 1/3.

Therefore, there are three numbers x, 1/2, and 1/3.

If their average is 1, we could write this as:

$\frac{x + \frac{1}{2} + \frac{1}{3} }{3} = 1 \\ x + \frac{1}{2} + \frac{1}{3} = 3(1) \\ x = 3 - \frac{1}{2} - \frac{1}{3}$

Let's multiple the whole equation to 2(3) to get rid of the denominators and for clearer simplification.

$(2 \times 3)x = 3(2 \times 3) - \frac{1}{2} (2 \times 3) - \frac{1}{ 3} (2 \times 3) \\ 6x = 18 - 3 - 2 \\ 6x = 13 \\ x = \frac{13}{6}$

To check:

$\frac{x + y + z}{3} = 1 \\ \frac{\frac{13}{6} + \frac{1}{2} + \frac{1}{3}}{3} = 1 \\ \frac{3}{3} = 1 \\ 1 = 1$