Ask a New Question
Menu

7 of 87 of 8 Items

Question
Given the equation 8(n+6)=104, identify the real-world problem that corresponds to this equation.(1 point)
Responses

Skip to navigation

page 18 of 18

3 answers

The equation \( 8(n + 6) = 104 \) can be interpreted in several real-world contexts. One possible scenario could be as follows:

Scenario: Party Planning

Imagine you are planning a party and need to arrange seating and catering. You discover that you need to set up tables for a certain number of guests.

  • Let \( n \) represent the number of additional guests you plan to invite beyond a base number.
  • The number 6 represents the 6 guests that you already have confirmed.
  • The 8 represents the number of tables you have available, and each table can accommodate \( n + 6 \) guests.
  • The total number of guests that can be accommodated at the party is 104.

Thus, the equation \( 8(n + 6) = 104 \) represents the situation where the total capacity of all available tables (8 tables seating \( n + 6 \) guests each) must equal the total number of guests you expect to host (104 guests).

In this way, the equation is grounded in a practical context of event management or planning.

Which equation corresponds to the following problem?
(1 point)
8(2n+6)=104
8(n+6)=104
2n+6=8
8+n+n+6=104

To determine which equation corresponds to the specified problem, we need to analyze the equations provided in relation to the problem context.

From your original equation \( 8(n + 6) = 104 \), we can see that it reflects a situation where there are 8 tables (or similar units), and each table accommodates \( n + 6 \) people, resulting in a total capacity of 104.

Now let's look at the options:

  1. \( 8(2n + 6) = 104 \): This suggests each of the 8 tables accommodates \( 2n + 6 \) people, which is different from our original equation.

  2. \( 8(n + 6) = 104 \): This is the original equation we started with, directly corresponding to the problem we have discussed.

  3. \( 2n + 6 = 8 \): This is a simplified version and does not resemble the original problem scenario.

  4. \( 8 + n + n + 6 = 104 \): This equation is more complex and involves additions of terms that do not directly correspond to the setup of our problem.

Based on the analysis, the equation that corresponds to the original problem context is:

\( 8(n + 6) = 104 \).

This would be the correct answer.