Author: wilsonn

From  https://www.nctm.org/

Grade 6-8

The Algenauts baseball team just finished a great year. During the season, they won three out of every four of their home games and two out of every three of their away games. All together they won 40 more games than they lost. If they played as many home games as away games, what was their final record of wins and losses?

Extension: In the playoffs, the Algenauts won their division playoff series 3 games to 1 and then beat their arch-rivals the Geometers in the League Championship series 4 games to 2. If the Algenauts won 80% of their home playoff games and 60% of their away playoff games, what percentage of their playoff games were at home?

Answer Check:

The Algenauts played a total of 96 games during the season. Be sure that you’ve determined their record of wins and losses, and that you used algebra to solve the problem.

If your answer doesn’t match ours:

• did you remember that they played half of their games at home and half of them away?
• did you consider the kind of numbers that would work with the fractions in the problem and result in whole numbers for the number of games?
• did you try guessing a total number of games and using the fractions to check the wins and losses in that case?
• did you try choosing a variable for your guess and using the calculations you made to check the guess to try and write an equation with the variable?
• did you check your arithmetic?

If any of those ideas help you, revise your answer. You can also leave a comment that tells what you changed and why you changed it. If you’re still stuck, leave a comment that tells where you’re having trouble.

If your answer does match ours,

• have you clearly shown and explained the work you did?
• did you make any mistakes along the way? If so, how did you find and fix them?
• are there any hints that you would give another student?
• are you confident that you could solve another problem like this successfully?

Revise your work if you have any ideas to add. Otherwise leave us a comment that tells us how you think you did – you might answer one or more of the questions above.