Write an inequality for each problem and solve. Heinrich is...

Write an inequality for each problem and solve. Heinrich is planning an Oktoberfest party at the House of Bratwurst, It costs $\$ 150.00$ to rent a tent plus $\$ 11.50$ per person for food. If Heinrich can spend at most $\$ 450.00$, find the greatest number of people he can invite to the party.

Write an inequality for each problem and solve.
Heinrich is planning an Oktoberfest party at the House of Bratwurst, It costs $\$ 150.00$ to rent a tent plus $\$ 11.50$ per person for food. If Heinrich can spend at most $\$ 450.00$, find the greatest number of people he can invite to the party.

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Key Concepts

Solving Linear Inequalities

Once the inequality is set up, the next step is to isolate the variable through algebraic manipulations such as addition, subtraction, multiplication, or division while maintaining the inequality's direction. This process yields a range of solutions that satisfy the inequality.

Interpreting Solutions with Integer Constraints

Often in practical scenarios, solutions must be adapted to meet specific requirements, such as variables that represent counts and must be whole numbers. This involves determining the maximum or minimum integer that satisfies the inequality, ensuring the solution is applicable in context.

Linear Inequalities

Linear inequalities involve expressions where two linear functions are related by inequality symbols such as <, >, ?, or ?. They are essential for modeling constraints and limits in various contexts by representing a range of acceptable values rather than a single value.

Translating Word Problems into Mathematical Models

This concept is about interpreting real-world scenarios and converting everyday language into algebraic expressions or inequalities. It requires identifying components such as fixed costs and variable costs, and then formulating a mathematical expression that accurately represents the problem's constraints.

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