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Solve the following real-world problem: Ahmadullah’s basketball team will play 21 games this season. That is 12 games more than 13 the number of games they played last season. How many games did they play last season?(1 point) Responses 7 games 7 games 27 games 27 games 11 games 11 games 33 games

whats the answer

3 answers

Let \( x \) be the number of games Ahmadullah's basketball team played last season. According to the problem, they will play 21 games this season, which is 12 games more than 13 times the number of games played last season.

We can express this as an equation:

\[ 21 = 13x + 12 \]

Now, we need to solve for \( x \).

  1. Start by subtracting 12 from both sides:

\[ 21 - 12 = 13x \]

This simplifies to:

\[ 9 = 13x \]

  1. Next, divide both sides by 13:

\[ x = \frac{9}{13} \]

The solution implies they played \(\frac{9}{13}\) games last season, which is not realistic in this context.

Instead, let's reinterpret the statement:

It means that this season's games \( (21) \) are 12 games more than the number of games last season. Thus, if the number of games last season is denoted as \( y \):

The equation would then be:

\[ 21 = y + 12 \]

Solving for \( y \):

  1. Subtract 12 from both sides:

\[ y = 21 - 12 \]

This simplifies to:

\[ y = 9 \]

This indicates that last season, Ahmadullah's basketball team played 9 games. However, since the options given do not contain 9 games, let’s check one more time with the approach of "12 more than last season's games":

\[ 21 - 12 = y \]

Which gives:

\[ y = 9 \]

Since none of the responses fit \( 9 \), please confirm whether there’s any miscommunication regarding the options, as the correct calculation leads to 9 games being played last season.

there is no 9 .....

I apologize for any confusion. Let's carefully reevaluate the original problem step by step:

The statement says that Ahmadullah’s basketball team will play 21 games this season, which is 12 games more than 13 times the number of games they played last season.

We can set up the equation based on the information given. Let \( x \) represent the number of games played last season.

According to the problem statement:

\[ 21 = 13x + 12 \]

Now we will solve for \( x \):

  1. Subtract 12 from both sides: \[ 21 - 12 = 13x \] \[ 9 = 13x \]

  2. Now divide by 13: \[ x = \frac{9}{13} \]

Since this result isn’t a whole number and doesn't correlate with the options provided, let’s rethink how we interpret the original conditions.

Looking again at the setup: Is it possible the problem should instead say that 21 games total are 12 fewer than a multiple (13-x)?

Let's take a different approach:

If they played \( y \) games last season, then:

\[ 21 = y + 12 \implies y = 21 - 12 \implies y = 9 \]

Since this leads to 9, your options of 7, 11, 27, and 33 don’t include it!

So if the interpretation is incorrect, can we instead figure it from the following method?

Upon double-checking the phrasing: Is it that:

  • 21 games = 12 more than last year's count. Confirming via standard values thereafter, we see no alignment.

In any case, it would appear I've thoroughly re-processed this incorrectly leading to the options available showing play styles such:

  • If examining ranges as per values we could correlate 12-13-more, which adjusts intriguingly.

But based on the original conditions, and the arithmetic checks through simple sought algebra reveals last year's must’ve been finessed through lenses of proportionality.

Could you confirm if the above approach is correct, helping reiterate assumptions or correct my misunderstandings again?

Thanks in advance!