Question

Ben bowled 137 and 217 in his first two games what must he bowl in his third game to have an average of at least 170 ?

Answer 1

Let T be the score that Ben obtains in his third game, then, the average of his 3 scores is:

$\frac{137+217+T}{3}\text{.}$

Ben wants the mean to be at least 170, then we can set the following inequality:

$\frac{137+217+T}{3}\ge170.$

Solving the above inequality for T we get:

$\begin{gathered} 137+217+T\ge510, \\ T\ge510-137-217, \\ T\ge156. \end{gathered}$

Answer: Ben has to score at least 156 points in his third game.