Question

At the end of last week, a baseball player’s average was .256. One week later, after getting 12 hits in 35 at-bats, the player’s average is now .275. How many hits and how many at-bats does the player now have for the season?

Answer 1

Let the player has x hits in y at-bats.

Since players initial average is 0.256, therefore, we can set up an equation:

`(x)/(y) =0.256`

Further, we are given that player hits 12 in 35 at-bats. Therefore, the total hits are now
`(x+12)` and total at-bats are now
`(y+35)`.

Since the new average becomes 0.275, therefore, we can set up:

`(x+12)/(y+35) =0.275`

Our next step is to solve these two equations and get values of x and y.

`(x)/(y)=0.256\Rightarrow x=0.256y\\ (x+12)/(y+35)=0.275\Rightarrow x+12=0.275y+9.625\\`

Upon using substitution method, we get:

`0.256y+12=0.275y+9.625\\ 0.275y-0.256y=12-9.625\\ 0.019y=2.375\\ y=(2.375)/(0.019)=125`

We can find the value of x by substituting this value of y in the first equation.

`x=0.256(125)\Rightarrow x=32`

Therefore, player made 32 hits in 125 at bats.