In the new lenox baseball tournament, the team played 3 games. in the first game they scored 18 runs in the second they scored 5 fewer runs than the third, and the tam scored less then 34 runs in all three games. what is the greatest number of runs they could have scored in the third game?

The greatest score could they have in the 3rd game is 10 runs

Step-by-step explanation:

- The team played 3 games

- In the first game they scored 18 runs

- In the second they scored 5 fewer runs than the third

- The team scored less then 34 runs in all three games

- We need to find the greatest number of runs they could have in

  the 3rd game

- Assume that the team scored x runs in the third game

∵ The team scored 18 runs in the 1st game

∵ The team scored x runs in the 3rd game

∵ The score of the 2nd game is 5 less than the third game

∴ The score of the 2nd game is x - 5 runs

- The team scored in the three games less than 34 runs

∵ The total score in the three games = 18 + x - 5 + x

∵ The total score is less than 34 runs

∴ 18 + x - 5 + x < 34

- Add the like terms in the L.H.S

∴ 2x + 13 < 34

- Subtract 13 from both sides

∴ 2x < 21

- Divide both sides by 2

∴ x < 10.5

∴ The greatest integer less than 10.5 is 10

∴ The greatest number of runs in the 3rd game is 10 runs

The greatest score could they have in the 3rd game is 10 runs

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