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

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 two variables:

\( c \) = number of children attending the party
\( a \) = number of adults attending the party

Now, we can set up the inequality based on the cost information provided:

The base cost is $150, which is a fixed cost. The cost per child is $10.50, so the total cost for children is \( 10.50c \). The cost per adult is $5.50, so the total cost for adults is \( 5.50a \).

The inequality that represents the total cost of the party staying within the $300 budget will then be:

\[ 150 + 10.50c + 5.50a \leq 300 \]

Given that at least one adult and one child must be at the party, we also have the conditions:

\( c \geq 1 \)
\( a \geq 1 \)

So, the complete representation would include:

\[ 150 + 10.50c + 5.50a \leq 300 \]
\[ c \geq 1 \]
\[ a \geq 1 \]

These constraints together will help Meha and her aunt understand how many children and adults can attend the party without exceeding the budget.

Answer 2

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

Yes because 10.5*10 + 5.5* 5 = 132.5 which is less than the $150