Question

the win to loss ratio for a baseball team is 5 : 6. for numbers 2a - 2d, circle yes or no to indicate whether each total number of wins, losses, or games is possible for the baseball team. 2a. 10 wins and 12 losses 2b. 20 wins and 44 games 2c. 12 wins and 13 losses 2d. 18 losses and 33 games

Explanation:

Step1: Analyze the ratio

The win - to - loss ratio is 5:6. So the number of wins is 5x, the number of losses is 6x, and the total number of games is 5x + 6x=11x, where x is a positive integer.

Step2: Check 2a

For 10 wins and 12 losses, $\frac{10}{12}=\frac{5}{6}$, so it is possible.

Step3: Check 2b

If there are 20 wins, since the number of wins is 5x, then 5x = 20, x = 4. The total number of games should be 11x=44. But if there are 20 wins and 44 games, the number of losses is 44 - 20 = 24, and $\frac{20}{24}
eq\frac{5}{6}$, so it is not possible.

Step4: Check 2c

$\frac{12}{13}
eq\frac{5}{6}$, so it is not possible.

Step5: Check 2d

If there are 18 losses, since the number of losses is 6x, then 6x = 18, x = 3. The total number of games is 11x = 33. So it is possible.

Answer:

2a. YES
2b. NO
2c. NO
2d. YES