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John and Jackie are planning a wedding. For the rehearsal dinner, they will have many guests. The cost to rent the restaurant is $475.00. The cost per person is $13.50. Let x represent the number of people. Write an inequality that John and Jackie can use to determine the total number of people allowed if they have only $785.00 to spend.



Answer :

JohnnyBarnwell

To determine the total number of people John and Jackie can invite to the rehearsal dinner given they have a budget of $785, we can create an inequality based on the given information.

Let's break it down step by step:

1. The cost to rent the restaurant is $475.00.

2. The cost per person is $13.50.

3. Let x represent the number of people John and Jackie can invite.

Based on the information above, the total cost of renting the restaurant and inviting x people can be represented as follows:

Total Cost = Cost of Renting Restaurant + Cost per Person * Number of People

This can be written as an inequality:

475 + 13.50x ≤ 785

Now, we need to solve this inequality to find the maximum number of people they can invite.

475 + 13.50x ≤ 785

Subtract 475 from both sides:

13.50x ≤ 310

Divide by 13.50 on both sides:

x ≤  310/13.50

x ≤ 22.96

Since the number of people must be a whole number, they can invite a maximum of 22 people to stay within their budget of $785.00.

semsee45

Answer:

[tex]475 + 13.5x \leq 785[/tex]

Step-by-step explanation:

To write an inequality representing the total number of people allowed given the budget constraint, we need to consider the total cost of the rehearsal dinner.

The fixed cost to rent the restaurant is $475.00

The cost per person is $13.50.

If x represents the number of people, then the total cost can be represented as:

[tex]475 + 13.5x[/tex]

Now, since John and Jackie have a maximum of $785.00 to spend, we can set the expression for the total cost to less than or equal to $785.00:

[tex]475 + 13.5x \leq 785[/tex]

Therefore, the inequality that John and Jackie can use to determine the total number of people allowed if they have only $785.00 to spend is:

[tex]\Large\boxed{\boxed{475 + 13.5x \leq 785}}[/tex]

[tex]\dotfill[/tex]

To solve this inequality, isolate x:

[tex]475 + 13.5x \leq 785\\\\\\13.5x \leq 785-475\\\\\\13.5x \leq 310\\\\\\x\leq \dfrac{310}{13.5}\\\\\\x\leq 22.96296296...[/tex]

Therefore, the maximum number of people John and Jackie can have at their wedding rehearsal dinner is 22.

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