2452.33 – Batting Average no. 2

We recall that a batting average of $.274$ means that $\frac{h}{b}=0.274$, which is almost certainly rounded from some long decimal.

So $\frac{h}{b}=0.274$, and $\frac{h+3}{b+4} = 0.289$ (again, rounded).

So we wheel up the algebra machine:

$h = 0.274b$ and $h+3 = 0.289(b+4) = 0.289b + 1.156$.

$0.274b + 3 = 0.289b + 1.156 \rightarrow 0.015b = 1.844$ ($= 3 - 1.156$)

$\rightarrow b = \frac{1.844}{0.015} = 122.933...$ Let's assume $123$.

Then $h = 0.274 x 123 = 33.702$. Let's assume $34$.

Checking, $\frac{34}{123}= 0.27642...$ So we've got rounding issues.

$0.276$ is a bit too big. Should we try $b = 124$ $\frac{34}{124}= 0.27419...$ That's pretty good.

And $\frac{34+3}{124+4} = 0.28906...$ Also pretty good.

If you start over using these 5-place decimals, you'll get $34$ and $124$ almost exactly.