omas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50 each, and a small bag of popcorn costs $4.50.
Emilio writes the inequality 17(f + 2) + 45.99 ≤ 200 to better represent the situation, using the variable f to represent the number of friends. Solve the inequality. Round your answer to the nearest hundredth. Then write the maximum number of friends that can attend the birthday party. Enter your answers in the boxes.
f ≤
Tomas and Emilio can invite
friends.
To solve the inequality, we need to perform the math operations.
First, distribute the 17 to both terms inside the parentheses:
17f + 17(2) + 45.99 ≤ 200
Then, simplify:
17f + 34 + 45.99 ≤ 200
Combine like terms:
17f + 79.99 ≤ 200
Next, subtract 79.99 from both sides of the inequality:
17f ≤ 120.01
Lastly, divide both sides of the inequality by 17 to solve for f:
f ≤ 7.06
Rounded to the nearest hundredth, f ≤ 7.
So, the maximum number of friends that can attend the birthday party is 7.
Therefore, Tomas and Emilio can invite 7 friends.