Let the player has x hits in y at-bats.
Since players initial average is 0.256, therefore, we can set up an equation:
[tex]\frac{x}{y} =0.256[/tex]
Further, we are given that player hits 12 in 35 at-bats. Therefore, the total hits are now [tex](x+12)[/tex] and total at-bats are now [tex](y+35)[/tex].
Since the new average becomes 0.275, therefore, we can set up:
[tex]\frac{x+12}{y+35} =0.275[/tex]
Our next step is to solve these two equations and get values of x and y.
[tex]\frac{x}{y}=0.256\Rightarrow x=0.256y\\ \frac{x+12}{y+35}=0.275\Rightarrow x+12=0.275y+9.625\\[/tex]
Upon using substitution method, we get:
[tex]0.256y+12=0.275y+9.625\\ 0.275y-0.256y=12-9.625\\ 0.019y=2.375\\ y=\frac{2.375}{0.019}=125[/tex]
We can find the value of x by substituting this value of y in the first equation.
[tex]x=0.256(125)\Rightarrow x=32[/tex]
Therefore, player made 32 hits in 125 at bats.
