Grade 9th middle school question the mean of 5 apple is $12$, the range of the biggest and the lowest is $6$. If every apple is subtracted by $a$ then the sum is divided by $b$, the new mean is $2$ and the range of the biggest and the lowest is $3$. Find $a$ and $b$.
 A: ok I am going to answer this question assuming that it is measuring a piece of information about the apple that has a mean of 12. It could be the number of apples in a batch, it could be the diameter, or radius but the answer will still be the same
So we have a data set: $\{v,w,x,y,z\}$
$v$ is the mesaurement of the first apple, $w$ is the measurement of the second apple and so on.
we know that the following
$\frac{v+w+x+y+z}{5}=12$ and $z-v=6$
when we do the changes, our new data set is: $\{\frac{v-a}{b},\frac{w-a}{b},\frac{x-a}{b},\frac{y-a}{b},\frac{z-a}{b}\}$
And we know that from that data set we have the following (I have simplified the equations):
$\frac{v+w+x+y+z-5a}{5b}=2$ and $\frac{z-v}{b}=3$
In the second one, we know that $z-v=6$ from the previous equation so we can substitute that in and find that $b=2$
We can also factor out the original mean from the third equation and get the following:
$\frac{1}{b}\times(\frac{v+w+x+y+z}{5}-\frac{5a}{5})=2$
We can substitute that mean inside with $12$ and $b$ with $2$
$\frac{1}{2}\times(12-a)=2$
$6-\frac{a}{2}=2$
$-\frac{a}{2}=-4$
$a=8$
Therefore we have found that $a, b=8,2$
If you need help understanding this just ask
