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
Let's define:
x = number of children attending the party
y = number of adults attending the party
Given that the cost for each child is $10.50 and the cost for each adult is $5.50, the total cost for the children would be 10.50x and the total cost for the adults would be 5.50y.
The total cost of the party is $150 plus the cost of the children and the adults, so the total cost can be represented as:
10.50x + 5.50y + 150
Since the aunt has budgeted $300 for the party and that is the maximum amount she wants to spend, we can set up an inequality:
10.50x + 5.50y + 150 ≤ 300
Therefore, the two-variable inequality that represents this situation is:
10.50x + 5.50y + 150 ≤ 300
Is it possible for the party to include 10 children and five adults? Use your inequality from part A to check. Explain your answer
To check whether it is possible for the party to include 10 children and five adults, we can substitute x = 10 and y = 5 into the inequality:
10.50x + 5.50y + 150 ≤ 300
Substituting the values:
10.50(10) + 5.50(5) + 150 ≤ 300
105 + 27.50 + 150 ≤ 300
282.50 + 150 ≤ 300
432.50 ≤ 300 (which is false)
Since the inequality is false, it means that including 10 children and five adults in the party exceeds the maximum budget of $300. Therefore, it is not possible for the party to include 10 children and five adults.