155k views
1 vote
Please help I’ve been stuck for a while

Jana scored 29 goals last hockey season. This hockey season, she scored 0 goals in 22 games, 1 goal in each of 16 games, and 2 goals in each of the remaining games. She scored fewer goals this season than last season. Which number line best represents all the possible numbers of games in which Jana scored 2 goals this season?

Please help I’ve been stuck for a while Jana scored 29 goals last hockey season. This-example-1
User PnP
by
7.1k points

1 Answer

2 votes

Final answer:

The number line represents 1 to 6 games in which Jana scored 2 goals each, as this is the range where the total number of goals does not exceed the maximum of 28 for this season.

Step-by-step explanation:

To determine the number of games in which Jana could have scored 2 goals, let's first calculate the total number of goals she scored this season other than the possible 2-goal games. She scored 0 goals in 22 games and 1 goal in 16 games:

  • 0 goals × 22 games = 0 goals
  • 1 goal × 16 games = 16 goals

Adding these together, Jana has scored 16 goals in games where she did not score 2 goals.

Since she scored 29 goals last season and this season she scored fewer, the maximum number of goals for this season is 28. Subtracting the 16 goals she scored in the 0-goal and 1-goal games from the maximum possible total for this season gives us:

28 goals (max this season) - 16 goals (already scored) = 12 goals

The remaining 12 goals must have come from games where she scored 2 goals each. Therefore, the number of 2-goal games is:

12 goals ÷ 2 goals/game = 6 games

Since she played a total of 22+16+x games this season, and the total number of games must be greater than the games where she scored 0 or 1 goal (which is 38), the number of 2-goal games, x, can range from 1 to 6.

The number line representing all the possible numbers of games where Jana scored 2 goals this season would start at 1 and end at 6, inclusively.

User Evgeniy Mikhalev
by
8.6k points