A catering company charges $300 plus $40 per guest for a wedding. Sarah and Eric do not want to spend more than $5,000 on catering. Write and solve an inequality in terms of the number of guests, g, that can be invited.
To find the inequality that represents the number of guests, g, that can be invited, we need to consider the cost restriction.
The catering company charges $300 plus $40 per guest. So, the total cost, C, can be represented as:
C = 300 + 40g
According to the problem, Sarah and Eric do not want to spend more than $5,000 on catering. Therefore, the inequality can be written as:
C ≤ 5000
Substituting the expression for C in terms of g, we have:
300 + 40g ≤ 5000
Simplifying the inequality, we get:
40g ≤ 4700
Dividing both sides of the inequality by 40, we find:
g ≤ 117.5
Therefore, the inequality representing the number of guests, g, that can be invited is:
g ≤ 117.5
However, since the number of guests must be a whole number, we round down the maximum number of guests:
g ≤ 117
Hence, Sarah and Eric can invite up to 117 guests to stay within their budget of $5,000.
To write the inequality, we need to set up the cost as an expression in terms of the number of guests, g, and then set it less than or equal to $5,000.
The cost of catering for the wedding can be expressed as $300 plus $40 per guest. So, the cost would be:
Cost = $300 + $40g
Now, we can set up the inequality to represent that the cost should be less than or equal to $5,000:
$300 + $40g ≤ $5,000
To solve this inequality for the number of guests, we can follow these steps:
1. Begin by subtracting $300 from both sides of the inequality to isolate the term with "g":
$40g ≤ $5,000 - $300
Simplifying further:
$40g ≤ $4,700
2. Next, divide both sides of the inequality by $40 to solve for "g":
g ≤ $4,700 ÷ $40
Simplifying further:
g ≤ 117.5
Since the number of guests can't be a decimal or fraction, we round down to the nearest whole number:
g ≤ 117
Therefore, in order for Sarah and Eric to not exceed the budget of $5,000, they can invite a maximum of 117 guests.