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

Answer:

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

Step-by-step explanation:

Averages are described by the following equations:

Initial average:

$\frac{x}{n} = 205$

$x = 205\cdot n$

Real average:

$\frac{x+241}{n+1} = 209$

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

$x = 209\cdot n - 32$

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

$4\cdot n = 32$

$n = 8$

$x = 205\cdot (8)$

$x = 1640$

Expected average:

$\frac{x+y}{n+1} = 211$

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

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

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

$y = 259$

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