The members of a bridge club are divided into tables of 4 to play bridge. There are 19 bridge tables at the club. What inequality expresses how many people can come to play on a given night?(1 point)

Question

Responses

p/4>19
Start Fraction p over 4 End Fraction greater than 19

4p≤19
4 p less-than-or-equal-to 19

p/4≤19
Start Fraction p over 4 End Fraction less-than-or-equal-to 19

p≤19/4

Answer 1

To find the inequality that expresses how many people can come to play on a given night at the bridge club, we first need to determine how many players can be accommodated at the 19 tables.

Since each table can seat 4 players, the total number of players that can be accommodated is:

\( 4 \times 19 = 76 \)

Thus, the number of players \( p \) should be less than or equal to 76. We can express this in inequality form as:

\( p \leq 76 \)

However, let's look at the options you've provided:

1. \( \frac{p}{4} > 19 \)
2. \( 4p \leq 19 \)
3. \( \frac{p}{4} \leq 19 \)
4. \( p \leq \frac{19}{4} \)

Among these options, the one that correctly represents the situation (but needs a little reformation) is option 3:

Option 3:

\( \frac{p}{4} \leq 19 \)

This does indeed represent the requirement that \( p \) (the number of players) should not exceed the total capacity of the tables. To see why this is true:

By multiplying both sides of the inequality \( \frac{p}{4} \leq 19 \) by 4, we obtain:

\( p \leq 76 \)

Thus, the correct interpretation of how many people can come to play on a given night is given by:

Final Answer: \( \frac{p}{4} \leq 19 \)