The inequality representing Nathaniel not wanting to spend more than $250 is 100 + 40x ≤ 250, where x is the number of people. Solving this inequality shows that Nathaniel can invite a maximum of 3 people to the dinner.
To represent the situation where Nathaniel is purchasing tickets for his friends and does not want to spend more than $250, we can write the following inequality:
100 + 40x ≤ 250
where x is the number of people Nathaniel is inviting.
To solve the inequality, we subtract $100 (the cost for one table) from both sides of the inequality:
40x ≤ 250 - 100
40x ≤ 150
Now, divide both sides by 40 to find the maximum number of people:
x ≤ 150 / 40
x ≤ 3.75
Since Nathaniel cannot invite a fraction of a person, the maximum number of people he can invite is 3.
the complete Question is given below:
BANQUET A charity is hosting a benefit dinner. They are asking $100 per table plus $40 per person. Nathaniel is purchasing tickets for his friends and does not wantto spend more than $250. a. Write an inequality to represent this situation, where x is the number of people. b. Solve the inequality. What is the maximum number of people Nathaniel can invite to the dinner?