Question

Ben bowled 153 and 201 in his first two games. What must he bowl in his third game to have an average of at least 170 ?

Answer 1

Let x be Ben's score in his third game, then if the average is at least 170 we get that:

$\frac{153+201+x}{3}\ge170.$

Multiplying the above inequality by 3 we get:

$\begin{gathered} \frac{153+201+x}{3}\cdot3\ge170\cdot3. \\ 153+201+x\ge510. \end{gathered}$

solving the above inequality for x we get:

$\begin{gathered} 354+x\ge510, \\ 354+x-354\ge510-354, \\ x\ge156. \end{gathered}$

Therefore x is at least 156.

Answer: He must bowl at least 156 in his third game in order to have an average of at least 170.