Question

Dana saved $450 for food for her upcoming vacation. The breakfast was included with their hotel, but lunch and dinner are not. When Dana cooks lunch or dinner it costs on average $10. When the family goes to a restaurant for lunch or dinner it costs on average $40. Let c represent meals that Dana cooks and let r represent meals the family goes to restaurants for. Write an inequality to represent the situation.

a) 10c + 40r ≤ 450
b) 10c + 40r ≥ 450
c) 10c - 40r ≤ 450
d) 10c - 40r ≥ 450

Answer 1

The inequality representing Dana's budget constraints for her vacation meals is 10c + 40r ≤ 450, where c is the number of cooked meals and r is the number of restaurant meals.

Step-by-step explanation:

The question involves creating an inequality to represent Dana's budget constraints for meals during her vacation. Since Dana saved a total of $450 for food and has the choice between cooking a meal that costs $10 (let c represent meals cooked) and going to a restaurant for a meal that costs on average $40 (let r represent restaurant meals), the correct inequality must represent the condition that the sum of cooked and restaurant meals does not exceed her total budget.

The inequality that correctly represents this situation is 10c + 40r ≤ 450. Option a) is correct because it suggests Dana can spend up to $450 on meals, whether she cooks them or eats out. It also shows the tradeoff between these options within her budget.