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

The two-variable inequality for Meha's cousin's birthday party budget is 150 + 10.5c + 5.5a ≤ 300, where c represents the number of children and a represents the number of adults attending the party.

Step-by-step explanation:

To represent the situation of planning a birthday party at the science center with a budget constraint using a two-variable inequality, we first need to define the variables:

• Let c be the number of children attending the party.
• Let a be the number of adults attending the party.

The cost for the party will be $150 for the venue, $10.50 for each child, and $5.50 for each adult. Since Meha's aunt has budgeted $300, our inequality will reflect the maximum amount she is willing to spend.

The inequality to represent the situation would be:

150 + 10.5c + 5.5a ≤ 300

This inequality shows that the total cost of the party, which is the sum of the base cost ($150) plus $10.50 per child and $5.50 per adult, should not exceed the budgeted amount of $300.