Home » » Let the mean of $$x, y^{-1}, z^{5}$$ be 6 find the mean of $$10, y^{-1}, 12, x, z^{5}$$....

# Let the mean of $$x, y^{-1}, z^{5}$$ be 6 find the mean of $$10, y^{-1}, 12, x, z^{5}$$....

### Question

Let the mean of $$x, y^{-1}, z^{5}$$ be 6 find the mean of $$10, y^{-1}, 12, x, z^{5}$$.

A) 7

B) 8

C) 9

D) 10

### Explanation:

Since the mean of $$x, y^{-1}$$ and $$z^5$$ is $$= 6$$
$$\therefore \cfrac{x+ y^{-1} + z^5 }{3} = 6$$
$$\therefore x + y^{-1} + z^5 = 6 \times 3 = 18$$
With this information, the mean of $$10, y^{-1}, 12, x$$ and $$z^5$$
$$= \cfrac{10+ y^{-1} + 12 + x + z^5}{5} = \text{M(mean)}$$
Substituting $$18$$ for $$x+y^{-1}+z^5$$
We then have $$\cfrac{10+12+18}{5} = M$$
$$\therefore \text{M} = \cfrac{40}{5}$$
$$\text{M} = 8$$
$$\therefore$$ the mean of $$10,y^{-1},12,x,z^5= 8$$

Explanation provided by Danny Babs

## Dicussion (1)

• Since the mean of $$x, y^{-1}$$ and $$z^5$$ is $$= 6$$
$$\therefore \cfrac{x+ y^{-1} + z^5 }{3} = 6$$
$$\therefore x + y^{-1} + z^5 = 6 \times 3 = 18$$
With this information, the mean of $$10, y^{-1}, 12, x$$ and $$z^5$$
$$= \cfrac{10+ y^{-1} + 12 + x + z^5}{5} = \text{M(mean)}$$
Substituting $$18$$ for $$x+y^{-1}+z^5$$
We then have $$\cfrac{10+12+18}{5} = M$$
$$\therefore \text{M} = \cfrac{40}{5}$$
$$\text{M} = 8$$
$$\therefore$$ the mean of $$10,y^{-1},12,x,z^5= 8$$