Question

Write and solve an inequality for each of the word problems.After two games of bowling, Brenda has a total score of 475. To win the tournament, she needs a total score of 684 or higher. Let x represent the score she needs for her third game to win the tournament. Write an inequality for x. What is the lowest score she can get for her third game and win the tournament?

Answer 1

It is given that the total score for the first two games is 475, and the score needed for the third game is x.

Hence, the total score for the three games will be:

`x+475`

Since the total score must be 684 or higher to win, it follows that the total score must be greater or equal to 684:

`x+475\ge684`

Solve the inequality by subtracting 475 from both sides:

`\begin{gathered} \Rightarrow x+475-475\ge684-475 \\ \Rightarrow x\ge209 \end{gathered}`

This implies that in order to win the game, she must score 209 or more in the third game.

It follows that the lowest score she can get to win is 209.

Answers:

The inequality for x is x+475 ≥ 684.

The solution to the inequality is x ≥ 209.

The lowest score she can get to win is 209.