Mike enters the Vermilion game with a batting average of .274. After going 3-for-4 in the game, his batting average jumps up to .289. How many hits did he have for the season before the Vermilion game began?
Solution
We recall that a batting average of .274 means that b=batsh=hits=0.274, which is almost certainly rounded from some long decimal.
So h=0.274b, and b+4h+3=0.289 (again, rounded). So we wheel up the algebra machine:
h+30.274b0.015bb=0.289(b+4)=0.289b+1.156=1.844=0.0151.844=122.933…
Let's assume 123. Then h=0.274×123=33.702. Let's assume 34.
Checking, 12334=0.27642… So we've got rounding issues. 0.276 is a bit too big.
Should we try b=124? 12434=0.27419… That's pretty good. And 124+434+3=0.28906… Also pretty good.
If you start over using these 5-place decimals, you'll get 34 and 124 almost exactly.