Meha is helping her aunt to plan a birthday party for her cousin at the science center. Her aunt tells her that the party will cost $150, plus $10.50 per child and $5.50 per adult. There needs to be at least one adult and at least one child at the party. She has budgeted $300 for the party and that is the maximum amount she wants to spend

Question

Meha is helping her aunt to plan a birthday party for her cousin at the science center. Her aunt tells her that the party will cost $150, plus $10.50 per child and $5.50 per adult. There needs to be at least one adult and at least one child at the party. She has budgeted $300 for the party and that is the maximum amount she wants to spend

Write a two-variable inequality to represent this situation. Be sure to define the variables you use in your inequality

Answer 1

Let's define:

x = number of children at the party
y = number of adults at the party

The cost of the party will be the sum of the base cost ($150) plus the cost per child ($10.50) multiplied by the number of children plus the cost per adult ($5.50) multiplied by the number of adults. The inequality representing this situation is:

150 + 10.50x + 5.50y ≤ 300

This inequality ensures that the total cost of the party (base cost + cost per child * number of children + cost per adult * number of adults) does not exceed $300.

Answer 2

B. Is it possible for the party to include 10 children and five adults? Use your inequality from part A to check. Explain your

Answer 3

To check if it is possible for the party to include 10 children and five adults, we substitute x = 10 and y = 5 into the inequality 150 + 10.50x + 5.50y ≤ 300:

150 + 10.50(10) + 5.50(5) ≤ 300
150 + 105 + 27.50 ≤ 300
282.50 ≤ 300

The inequality is true, because 282.50 is less than or equal to 300. Therefore, it is possible for the party to include 10 children and five adults while staying within the budget of $300.