Answer :
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:
[tex] \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}[/tex]
Let's multiple the whole equation to 2(3) to get rid of the denominators and for clearer simplification.
[tex](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} [/tex]
To check:
[tex] \frac{x + y + z}{3} = 1 \\ \frac{\frac{13}{6} + \frac{1}{2} + \frac{1}{3}}{3} = 1 \\ \frac{3}{3} = 1 \\ 1 = 1[/tex]