Question

In his last game of bowling, Roberto earned a score of 241, and his average score increased from 205 to 209. What score would he have needed in the last game to increase his average to 211?

Answer 1

Robert would have needed 259 point to increase his average to 211.

Explanation:

Averages are described by the following equations:

Initial average:

`(x)/(n) = 205`

`x = 205\cdot n`

Real average:

`(x+241)/(n+1) = 209`

`x + 241 = 209\cdot n + 209`

`x = 209\cdot n - 32`

`205\cdot n = 209\cdot n - 32`

`4\cdot n = 32`

`n = 8`

`x = 205\cdot (8)`

`x = 1640`

Expected average:

`(x+y)/(n+1) = 211`

`x + y = 211\cdot n+211`

`y = 211\cdot n + 211 - x`

`y = 211\cdot (8) + 211 - 1640`

`y = 259`

Robert would have needed 259 point to increase his average to 211.