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 ave…

Question

asked Aug 25, 2021 175k views

1 Answer

Mirel · Answer 1 · 2021-08-30T09:14:59+0000

Answer:

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.